id string | setting_key string | messages list | ground_truth string | dataset string |
|---|---|---|---|---|
algebra_func_area_train_0700 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = (-3(5(1cos(1π(-1x - 3) + 1) + 1)^2 + 1(1cos(1π(-1x - 3) + 1) + 1) - 4) - 3)/(2(5(1cos(1π(-1x - 3) + 1) + 1)^2 + 1(1cos(1π(-1x - 3) + 1) + 1) - 4) + 2) and g(x) = -4((3(1|x| - 2) + 1)/(3(1|x| - 2) - 2))^2 + 1((3(1|x| - 2) ... | 8.5 | MATH_EXPLORATIVE |
algebra_func_area_train_0701 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = 1|(-3(-1sin(2πx + 1) + 1) + 3)|, g(x) = (3(2|x + 1| - 1))/(-1(2|x + 1| - 1) + 2), x = -1.7, and x = -1.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.0 | MATH_EXPLORATIVE |
algebra_func_area_train_0702 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = (-1(2(3|(1x^2 + 3x - 3) - 2|) + 4) - 3)/(-3(2(3|(1x^2 + 3x - 3) - 2|) + 4) - 1), g(x) = -2sin(1π(4(1x - 3)^2 + 5(1x - 3) - 2) + 3) + 1, x = -4.9, and x = -4.8. Round your answer to 1 decimal place.\n\nPresent the answer i... | 0.1 | MATH_EXPLORATIVE |
algebra_func_area_train_0703 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = (-1(-5(-3x^2 - 3x + 5)) + 2)/(2(-5(-3x^2 - 3x + 5)) + 3), g(x) = 4(-5x^2 - 3x + 4) - 2, x = -1.8, and x = -1.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 7.7 | MATH_EXPLORATIVE |
algebra_func_area_train_0704 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = 3|(2(-4(-2sin(3πx + 2) + 1) + 4)^2 - 1) - 3| - 2 and g(x) = 4(-1|(-1x^2 + 3x + 1) - 2| + 1) + 2 between the vertical lines x = 3.1 and x = 3.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\b... | 4.3 | MATH_EXPLORATIVE |
algebra_func_area_train_0705 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = 1|(2(2e^(-1x) - 1)^2 + 5(2e^(-1x) - 1) + 3) - 1| + 2 and g(x) = -3sin(2π((2x)/(-3x + 2)) - 1) + 1 between the vertical lines x = 0.8 and x = 0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \... | 0.3 | MATH_EXPLORATIVE |
algebra_func_area_train_0706 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = (-2(1e^(-2x) + 3) + 2)/(3(1e^(-2x) + 3) - 1) and g(x) = -1|x - 1| between the vertical lines x = 0.5 and x = 1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.3 | MATH_EXPLORATIVE |
algebra_func_area_train_0707 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = (1(4x - 4) - 2)/(-3(4x - 4)), g(x) = -2|x - 1| + 1, x = 1.2, and x = 1.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.0 | MATH_EXPLORATIVE |
algebra_func_area_train_0708 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = 1|((1(-1(-4x^2 + 5x + 2) - 5) - 3)/(-3(-1(-4x^2 + 5x + 2) - 5) + 4)) + 3| - 1 and g(x) = -1((2(-1x^2 + 2x + 2) - 2)/(-3(-1x^2 + 2x + 2) - 3)) + 2 between the vertical lines x = -0.7 and x = 2.2. Round to 1 decima... | 2.2 | MATH_EXPLORATIVE |
algebra_func_area_train_0709 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = -4(3cos(1πx + 1) - 2)^2 - 5(3cos(1πx + 1) - 2) - 2 and g(x) = -2x^2 + 3x - 2 from x = 3.1 to x = 4.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 14.6 | MATH_EXPLORATIVE |
algebra_func_area_train_0710 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = -1cos(1π(-3x - 3) + 1) - 1 and g(x) = -1|x + 1| + 2 from x = -4.9 to x = -4.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.0 | MATH_EXPLORATIVE |
algebra_func_area_train_0711 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = -1((1(2|(-2x^2 + 2x + 1) + 3| - 3) + 3)/(1(2|(-2x^2 + 2x + 1) + 3| - 3) + 1)) - 3, g(x) = (2(-5(1sin(1πx - 2) + 2) + 1) - 2)/(-1(-5(1sin(1πx - 2) + 2) + 1) - 1), x = -1.1, and x = -0.9. Round your answer to 1 decimal plac... | 0.1 | MATH_EXPLORATIVE |
algebra_func_area_train_0712 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = -2sin(2π(-3x^2 - 4x - 1) - 2) + 1 and g(x) = 2x between the vertical lines x = 1.0 and x = 1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.1 | MATH_EXPLORATIVE |
algebra_func_area_train_0713 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = -1(-2|((-3(2x^2 - 5x) + 2)/(-2(2x^2 - 5x) - 3)) - 1| + 3) - 1, g(x) = (2(2cos(3π(-5x^2 - 2x - 5) + 3) - 2) - 2)/(1(2cos(3π(-5x^2 - 2x - 5) + 3) - 2) - 2), x = 1.4, and x = 1.5. Round your answer to 1 decimal place.\n\nPre... | 0.0 | MATH_EXPLORATIVE |
algebra_func_area_train_0714 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = 1((-3(4x - 1) + 2)/(2(4x - 1) + 3))^2 - 1((-3(4x - 1) + 2)/(2(4x - 1) + 3)) - 5, g(x) = -4(-3sin(2πx - 1))^2 - 1(-3sin(2πx - 1)) + 1, x = -3.3, and x = -2.9. Round your answer to 1 decimal place.\n\nPresent the answer in ... | 9.3 | MATH_EXPLORATIVE |
algebra_func_area_train_0715 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = 1|(5x^2 + 5x) - 3| - 1 and g(x) = 1x^2 - 1x - 1 from x = -1.9 to x = -1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 1.4 | MATH_EXPLORATIVE |
algebra_func_area_train_0716 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = 2(3sin(3π(-1x + 2) + 2) - 3)^2 - 5(3sin(3π(-1x + 2) + 2) - 3) + 1 and g(x) = 3(-2x^2 - 2x + 5) + 3 from x = -2.0 to x = -1.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.5 | MATH_EXPLORATIVE |
algebra_func_area_train_0717 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = (-1(1x^2 - 1x + 3) + 3)/(-1(1x^2 - 1x + 3)) and g(x) = 3|x - 3| - 2 between the vertical lines x = 2.2 and x = 3.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2.3 | MATH_EXPLORATIVE |
algebra_func_area_train_0718 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = -2|(-4(5x^2 - 1x - 3) + 2) - 1| + 3, g(x) = -2e^(1(4x^2 - 1x + 1)) - 1, x = -0.4, and x = 0.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 11.7 | MATH_EXPLORATIVE |
algebra_func_area_train_0719 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = 2|(-4((2(-1cos(3πx + 3)) + 2)/(-1(-1cos(3πx + 3)))) + 4) + 2| - 1 and g(x) = -2(1|((-3x - 3)/(-2x + 3))| - 3)^2 + 2 from x = 4.9 to x = 5.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your an... | 0.5 | MATH_EXPLORATIVE |
algebra_func_area_train_0720 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = 2cos(2π((-3(1x + 1) - 3)/(2(1x + 1) - 3))) and g(x) = -5(2sin(3πx + 1) - 1)^2 + 3(2sin(3πx + 1) - 1) from x = -3.9 to x = -3.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.1 | MATH_EXPLORATIVE |
algebra_func_area_train_0721 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = 1sin(1π(-1x^2 - 5x + 3) - 3) + 2, g(x) = -3|x + 1| + 3, x = -1.4, and x = -1.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.1 | MATH_EXPLORATIVE |
algebra_func_area_train_0722 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = 3sin(3π((-2(-1(5x^2 + 4x + 1) + 2) + 2)/(1(-1(5x^2 + 4x + 1) + 2) + 3))) and g(x) = (-2(3|(-2x^2 - 1x + 2) + 1| + 2))/(2(3|(-2x^2 - 1x + 2) + 1| + 2) - 3) between the vertical lines x = -1.8 and x = -1.7. Round t... | 0.2 | MATH_EXPLORATIVE |
algebra_func_area_train_0723 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1cos(1π(3x - 2) - 3) and g(x) = 3x - 5 between the vertical lines x = 1.5 and x = 1.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.2 | MATH_EXPLORATIVE |
algebra_func_area_train_0724 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = 2|((-3(-1cos(1πx - 2) - 3) + 1)/(1(-1cos(1πx - 2) - 3) + 3)) - 2| + 3 and g(x) = 1((2x)/(-1x - 2))^2 - 2((2x)/(-1x - 2)) + 2 between the vertical lines x = -4.6 and x = -4.1. Round to 1 decimal place.\n\nPresent ... | 3.9 | MATH_EXPLORATIVE |
algebra_func_area_train_0725 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = -5(-4(3cos(2π(-2|x| - 2) + 3) - 2)^2 + 3(3cos(2π(-2|x| - 2) + 3) - 2) + 4) + 4 and g(x) = -1(3(-1|x + 1| - 1)^2 + 2(-1|x + 1| - 1) + 5) - 1 between the vertical lines x = 0.2 and x = 0.3. Round to 1 decimal place... | 0.3 | MATH_EXPLORATIVE |
algebra_func_area_train_0726 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = -2((-1(1|(-1x + 4) + 2| + 2) + 3)/(2(1|(-1x + 4) + 2| + 2) - 3))^2 - 1((-1(1|(-1x + 4) + 2| + 2) + 3)/(2(1|(-1x + 4) + 2| + 2) - 3)) - 3, g(x) = -1|(3(-5x^2 + 2x + 5))| - 2, x = 1.2, and x = 1.3. Round your answer to 1 de... | 0.1 | MATH_EXPLORATIVE |
algebra_func_area_train_0727 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = 1(-2|(1((-1x - 3)/(-3x - 2))^2 - 4((-1x - 3)/(-3x - 2)) - 1) + 2| + 2) + 4, g(x) = (2(3(3e^(-1x))^2 + 2(3e^(-1x)) + 1) + 3)/(-1(3(3e^(-1x))^2 + 2(3e^(-1x)) + 1) - 2), x = -1.5, and x = -0.5. Round your answer to 1 decimal... | -8.8 | MATH_EXPLORATIVE |
algebra_func_area_train_0728 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = 1((-3(1|(1x - 4) - 3| + 2) - 3)/(3(1|(1x - 4) - 3| + 2) + 3))^2 - 2((-3(1|(1x - 4) - 3| + 2) - 3)/(3(1|(1x - 4) - 3| + 2) + 3)) + 3 and g(x) = -1(-1(-2cos(1πx + 2) - 2)^2 - 3(-2cos(1πx + 2) - 2) - 5) + 1 from x = -1.6 to ... | 0.8 | MATH_EXPLORATIVE |
algebra_func_area_train_0729 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = -4((2(4(2|x - 2|)^2 - 3(2|x - 2|) - 2))/(3(4(2|x - 2|)^2 - 3(2|x - 2|) - 2) + 2)) - 1, g(x) = -5(2sin(2π((-3x)/(-3x + 2)) + 1) - 3) + 4, x = 1.5, and x = 2.5. Round your answer to 1 decimal place.\n\nPresent the answer in... | 30.7 | MATH_EXPLORATIVE |
algebra_func_area_train_0730 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = -2(-1((3(-1|x - 2| + 1) + 2)/(-2(-1|x - 2| + 1))) - 4)^2 - 3(-1((3(-1|x - 2| + 1) + 2)/(-2(-1|x - 2| + 1))) - 4) + 3 and g(x) = 1sin(3π(-2((1x - 1)/(2x - 1)) - 5) - 3) + 3 from x = 2.0 to x = 2.6. Round to 1 decimal place... | 0.6 | MATH_EXPLORATIVE |
algebra_func_area_train_0731 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = (2(4(2x^2 + 4x) - 3) - 2)/(-3(4(2x^2 + 4x) - 3) - 2) and g(x) = -4(-1x)^2 + 1(-1x) + 5 from x = -2.1 to x = -1.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 3.3 | MATH_EXPLORATIVE |
algebra_func_area_train_0732 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = (3(1e^(-2(-2|x + 1| + 3)) - 3))/(2(1e^(-2(-2|x + 1| + 3)) - 3) + 2) and g(x) = -3|(1sin(3πx - 3) + 3) - 3| + 2 between the vertical lines x = 4.0 and x = 4.3. Round to 1 decimal place.\n\nPresent the answer in La... | 0.5 | MATH_EXPLORATIVE |
algebra_func_area_train_0733 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = -3sin(1π(-3|(3((2x - 1)/(-1x - 3)) - 2) - 3| + 3) - 1) - 3 and g(x) = -4(1((2x - 1)/(-2x - 2)) + 4)^2 + 5(1((2x - 1)/(-2x - 2)) + 4) between the vertical lines x = -2.4 and x = -2.3. Round to 1 decimal place.\n\n... | 0.2 | MATH_EXPLORATIVE |
algebra_func_area_train_0734 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = -4(-2cos(1πx + 1) + 3) + 2 and g(x) = -5x^2 + 2x - 2 between the vertical lines x = -0.2 and x = 1.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 13.3 | MATH_EXPLORATIVE |
algebra_func_area_train_0735 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = 3e^(-2(3|x - 1|)) - 1 and g(x) = (2x + 1)/(1x + 3) from x = -1.3 to x = 0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2.2 | MATH_EXPLORATIVE |
algebra_func_area_train_0736 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = 1(1e^(-1(3|((-1x + 2)/(-1x - 1)) + 3| - 3)) + 1) + 2 and g(x) = -3sin(1π((1(2x + 4) + 1)/(1(2x + 4) - 2)) + 1) from x = -1.8 to x = -1.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answe... | 1.2 | MATH_EXPLORATIVE |
algebra_func_area_train_0737 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = -4(1cos(1πx + 3) - 1) + 5 and g(x) = 3|x - 2| between the vertical lines x = -2.1 and x = -1.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.4 | MATH_EXPLORATIVE |
algebra_func_area_train_0738 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = (-1(-2|(-5x + 3) + 3|) + 2)/(-3(-2|(-5x + 3) + 3|) - 2) and g(x) = 3|(-3x^2 + 3x + 5) + 1| + 3 between the vertical lines x = 1.1 and x = 1.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\bo... | 8.0 | MATH_EXPLORATIVE |
algebra_func_area_train_0739 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = 4(1|((3x + 1)/(-2x - 1)) + 1| + 1) - 3, g(x) = -5(-1|x + 1| - 2) - 5, x = -1.0, and x = -0.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.0 | MATH_EXPLORATIVE |
algebra_func_area_train_0740 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = -3(5(-3sin(3π(1|x| + 2) - 2) - 1) + 5)^2 + 2(5(-3sin(3π(1|x| + 2) - 2) - 1) + 5) - 2 and g(x) = -3sin(1π((-1(3|x + 1| - 3) - 2)/(-1(3|x + 1| - 3) - 2)) - 3) - 2 from x = -0.6 to x = -0.5. Round to 1 decimal place.\n\nPres... | 4.7 | MATH_EXPLORATIVE |
algebra_func_area_train_0741 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = -3|(5(1cos(3πx + 1))^2 - 2(1cos(3πx + 1)) + 5) - 3| + 2 and g(x) = 2(5x - 1)^2 - 5(5x - 1) - 5 between the vertical lines x = 0.5 and x = 0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\bo... | 0.6 | MATH_EXPLORATIVE |
algebra_func_area_train_0742 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = 1sin(3π((2(1|(3x + 2) - 1| - 3) + 1)/(-1(1|(3x + 2) - 1| - 3) + 2)) - 3) and g(x) = -1e^(-1((-3(-4x^2 + 2x - 4) - 3)/(-1(-4x^2 + 2x - 4) + 2))) from x = -1.7 to x = -1.5999999999999999. Round to 1 decimal place.\n\nPresen... | 0.1 | MATH_EXPLORATIVE |
algebra_func_area_train_0743 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = 1(4((-2x + 1)/(3x))^2 - 3((-2x + 1)/(3x)) - 4) - 4, g(x) = (1(5x^2 - 1x - 3) + 3)/(3(5x^2 - 1x - 3) + 1), x = 0.1, and x = 0.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your ans... | 5.0 | MATH_EXPLORATIVE |
algebra_func_area_train_0744 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = -1(-2|(-3(-3sin(3πx - 3) + 1)^2 - 2(-3sin(3πx - 3) + 1) - 3) + 2| + 1) - 4 and g(x) = (-2(-3(3|x - 2| + 2) + 1) + 3)/(-2(-3(3|x - 2| + 2) + 1) + 1) from x = 0.3 to x = 0.4. Round to 1 decimal place.\n\nPresent the answer ... | 0.5 | MATH_EXPLORATIVE |
algebra_func_area_train_0745 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = 1cos(1π(-1(2|x + 2| - 1)) + 2) + 3 and g(x) = 4((-1x + 2)/(3x - 2)) + 3 between the vertical lines x = 4.2 and x = 4.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.0 | MATH_EXPLORATIVE |
algebra_func_area_train_0746 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = -4((-1x + 2)/(-2x - 1))^2 - 5((-1x + 2)/(-2x - 1)) - 2 and g(x) = (-1x)/(1x) between the vertical lines x = 0.3 and x = 1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
... | 0.3 | MATH_EXPLORATIVE |
algebra_func_area_train_0747 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = 2cos(1π(3((2(4x - 1) + 1)/(-2(4x - 1) - 3))^2) + 3) + 1 and g(x) = -2(-1|(-3sin(1πx + 3))| - 1)^2 + 3 between the vertical lines x = 1.0 and x = 1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex forma... | 0.1 | MATH_EXPLORATIVE |
algebra_func_area_train_0748 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = 3sin(1π(2|(-4x - 3) - 2| + 3)) + 1 and g(x) = -1|(-2x + 4) + 3| - 1 from x = 3.3 to x = 3.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.6 | MATH_EXPLORATIVE |
algebra_func_area_train_0749 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = -3(1e^(2(-2|(1x^2 + 4)| + 3)) - 3) - 5 and g(x) = 1(-2e^(-1(3|x + 3| - 1)) - 1)^2 - 3(-2e^(-1(3|x + 3| - 1)) - 1) - 4 from x = -3.7 to x = -2.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{You... | 20.0 | MATH_EXPLORATIVE |
algebra_func_area_train_0750 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = -2((2(1e^(1x) + 3))/(-1(1e^(1x) + 3) - 2)) + 5 and g(x) = (1(-1|x + 2| + 1) + 3)/(-3(-1|x + 2| + 1)) from x = -3.1 to x = -0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 43.4 | MATH_EXPLORATIVE |
algebra_func_area_train_0751 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = -3sin(1π(-2x^2 - 3x - 3) + 2) and g(x) = (-1x + 2)/(1x) from x = 2.7 to x = 2.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.2 | MATH_EXPLORATIVE |
algebra_func_area_train_0752 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = -2(4x - 4)^2 + 5(4x - 4) - 3 and g(x) = -1x^2 - 5x between the vertical lines x = 0.9 and x = 2.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 6.4 | MATH_EXPLORATIVE |
algebra_func_area_train_0753 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = -3cos(3π(1|(-5((-2x - 3)/(-1x - 1))^2 + 1((-2x - 3)/(-1x - 1)) - 3)| - 2) + 1) + 3, g(x) = -2sin(1π(2|(-2x^2 + 2x + 5) - 3| - 1) - 1) + 3, x = 1.5, and x = 1.6. Round your answer to 1 decimal place.\n\nPresent the answer ... | 0.3 | MATH_EXPLORATIVE |
algebra_func_area_train_0754 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = 1|((-2(-1(-5x - 4)^2 + 5(-5x - 4) + 4) + 1)/(-3(-1(-5x - 4)^2 + 5(-5x - 4) + 4) + 4)) - 2| - 3 and g(x) = -5((1(-2|x| + 3))/(-3(-2|x| + 3) - 3)) + 4 from x = -1.9 to x = -0.7. Round to 1 decimal place.\n\nPresent the answ... | 7.1 | MATH_EXPLORATIVE |
algebra_func_area_train_0755 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = -2|(4(-1x - 3)^2 + 4(-1x - 3) + 2)| and g(x) = -4(-3cos(1πx + 3) + 2)^2 + 4(-3cos(1πx + 3) + 2) from x = -2.8 to x = -2.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.5 | MATH_EXPLORATIVE |
algebra_func_area_train_0756 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = (2(-1|(3(4x - 4)^2 + 2(4x - 4) - 4) + 2| + 2) + 3)/(2(-1|(3(4x - 4)^2 + 2(4x - 4) - 4) + 2| + 2) - 3) and g(x) = 5(-1|((-1x + 3)/(3x + 1)) - 2|)^2 + 5 between the vertical lines x = 1.1 and x = 1.2. Round to 1 de... | 5.2 | MATH_EXPLORATIVE |
algebra_func_area_train_0757 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = (-1(1cos(1πx + 3) + 1) + 2)/(-3(1cos(1πx + 3) + 1) + 2) and g(x) = -2|x + 2| - 3 between the vertical lines x = 3.6 and x = 4.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answe... | 15.4 | MATH_EXPLORATIVE |
algebra_func_area_train_0758 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = -2e^(-1(-2|x + 2|)) + 3 and g(x) = -3x^2 - 1x - 4 between the vertical lines x = -3.5 and x = -1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 28.8 | MATH_EXPLORATIVE |
algebra_func_area_train_0759 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1((-1(1cos(2π(-5x^2 + 2x + 3) + 3)))/(-3(1cos(2π(-5x^2 + 2x + 3) + 3)) + 2)) - 5 and g(x) = -2(-2cos(3π(-2|x + 2| + 3) - 2) + 3) + 2 between the vertical lines x = -4.0 and x = -3.9. Round to 1 decimal place.\n\... | 0.3 | MATH_EXPLORATIVE |
algebra_func_area_train_0760 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = (-2(3(1sin(3π(2|x + 1| - 1) - 1) - 1)^2 - 5(1sin(3π(2|x + 1| - 1) - 1) - 1) - 3) - 2)/(2(3(1sin(3π(2|x + 1| - 1) - 1) - 1)^2 - 5(1sin(3π(2|x + 1| - 1) - 1) - 1) - 3) + 3), g(x) = 4(-3sin(3π(-1x + 5) + 1) + 1)^2 + 4(-3sin(... | 0.7 | MATH_EXPLORATIVE |
algebra_func_area_train_0761 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = 2((2x - 1)/(-1x - 2)) and g(x) = -3|x - 1| + 2 between the vertical lines x = 0.4 and x = 2.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2.5 | MATH_EXPLORATIVE |
algebra_func_area_train_0762 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1e^(1(4x + 1)) + 3 and g(x) = -2x - 3 between the vertical lines x = -3.0 and x = 0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 8.7 | MATH_EXPLORATIVE |
algebra_func_area_train_0763 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = 1(-1cos(3π((-1x + 2)/(-3x + 1))) + 1) - 1 and g(x) = (2(-1x^2 - 1x + 1) + 2)/(2(-1x^2 - 1x + 1)) from x = 0.8 to x = 1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.1 | MATH_EXPLORATIVE |
algebra_func_area_train_0764 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(-2e^(2(-1((2x - 2)/(3x - 2))^2 + 1((2x - 2)/(3x - 2)) - 4)) + 2) - 5 and g(x) = (-2(-2|(4x - 3)|) - 2)/(2(-2|(4x - 3)|) + 1) between the vertical lines x = 0.7 and x = 0.8. Round to 1 decimal place.\n\nPresent ... | 0.1 | MATH_EXPLORATIVE |
algebra_func_area_train_0765 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = 4(-2sin(2πx - 1) - 1) and g(x) = (1x - 1)/(2x + 1) between the vertical lines x = -0.4 and x = 0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 1.5 | MATH_EXPLORATIVE |
algebra_func_area_train_0766 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = (-3(2cos(3πx - 1) - 2) + 2)/(-3(2cos(3πx - 1) - 2) - 1) and g(x) = -1|x - 1| + 3 from x = -4.6 to x = -4.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.2 | MATH_EXPLORATIVE |
algebra_func_area_train_0767 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = -3|(1(3(3cos(1πx + 1) + 1)^2 - 2(3cos(1πx + 1) + 1) - 3) + 1) - 3| - 3 and g(x) = -1(-2e^(1(1|x - 2| - 1)) + 2) - 3 between the vertical lines x = 1.2 and x = 1.3. Round to 1 decimal place.\n\nPresent the answer ... | 0.5 | MATH_EXPLORATIVE |
algebra_func_area_train_0768 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1((-1(-1x^2 - 4x + 5))/(2(-1x^2 - 4x + 5) + 2)) - 2 and g(x) = 2((2x - 2)/(3x)) between the vertical lines x = 0.4 and x = 1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answe... | 3.5 | MATH_EXPLORATIVE |
algebra_func_area_train_0769 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = 5(1cos(2π(1|x + 2| + 1) + 3))^2 + 4(1cos(2π(1|x + 2| + 1) + 3)) - 4, g(x) = -3|(-4x^2 + 2x + 5)|, x = -0.7, and x = 1.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
... | 20.5 | MATH_EXPLORATIVE |
algebra_func_area_train_0770 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = 2(1cos(1π(4x^2 + 1x + 5) + 3) + 2) + 2 and g(x) = (1(2cos(1πx - 2) - 3) + 3)/(2(2cos(1πx - 2) - 3) + 3) between the vertical lines x = 2.8 and x = 4.4. Round to 1 decimal place.\n\nPresent the answer in LaTex for... | 13.6 | MATH_EXPLORATIVE |
algebra_func_area_train_0771 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = -3|(3x + 1)| and g(x) = -2x - 4 from x = -0.6 to x = 0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 1.3 | MATH_EXPLORATIVE |
algebra_func_area_train_0772 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = 1|(-3cos(2πx + 1) + 3)| + 3 and g(x) = -3x between the vertical lines x = -1.9 and x = -1.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 1.6 | MATH_EXPLORATIVE |
algebra_func_area_train_0773 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = 4((-3x + 3)/(2x + 1))^2 + 5((-3x + 3)/(2x + 1)) - 2 and g(x) = 2x^2 - 5x - 2 from x = -2.1 to x = 2.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | -34.6 | MATH_EXPLORATIVE |
algebra_func_area_train_0774 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = -4((1(1x^2 + 3x + 2) - 1)/(-3(1x^2 + 3x + 2) - 2)) + 4 and g(x) = (-3(2cos(1πx - 1) - 3) - 1)/(-2(2cos(1πx - 1) - 3) - 2) between the vertical lines x = 0.5 and x = 2.2. Round to 1 decimal place.\n\nPresent the a... | 4.8 | MATH_EXPLORATIVE |
algebra_func_area_train_0775 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = 4(1|x - 2| - 3) + 1, g(x) = -1x + 2, x = -1.7, and x = 4.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 32.3 | MATH_EXPLORATIVE |
algebra_func_area_train_0776 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = (-2(1(-1|(2x^2 - 3x + 2) + 1| + 3) + 5) + 2)/(2(1(-1|(2x^2 - 3x + 2) + 1| + 3) + 5) + 2) and g(x) = 1sin(1π(-2(-2|x + 2| + 3)^2) + 3) from x = 1.9 to x = 2.0. Round to 1 decimal place.\n\nPresent the answer in LaTex forma... | 0.1 | MATH_EXPLORATIVE |
algebra_func_area_train_0777 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = 3sin(3π(5x^2 + 5x + 5)) and g(x) = 3x - 1 from x = 1.0 to x = 1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.3 | MATH_EXPLORATIVE |
algebra_func_area_train_0778 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = -2sin(1π(2x + 5) + 1) - 3, g(x) = -1|x + 1| + 3, x = 4.3, and x = 4.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.8 | MATH_EXPLORATIVE |
algebra_func_area_train_0779 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = (1(1e^(-1x) - 3) - 2)/(1(1e^(-1x) - 3) - 3), g(x) = 1|x|, x = -0.7, and x = 0.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.6 | MATH_EXPLORATIVE |
algebra_func_area_train_0780 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = 1sin(1π(-2x^2 + 1x - 2) + 1) + 1, g(x) = 5x + 5, x = -0.9, and x = -0.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.1 | MATH_EXPLORATIVE |
algebra_func_area_train_0781 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = (-1(1(-1|(-2x^2 - 3x - 2)| - 3)) + 1)/(2(1(-1|(-2x^2 - 3x - 2)| - 3)) - 1) and g(x) = (-2(-2|(4x - 3) - 3| + 2))/(-1(-2|(4x - 3) - 3| + 2) + 2) from x = 1.3 to x = 1.7. Round to 1 decimal place.\n\nPresent the answer in L... | 20.6 | MATH_EXPLORATIVE |
algebra_func_area_train_0782 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = (-2(3(1x + 3)^2 + 3(1x + 3) - 5) - 2)/(-1(3(1x + 3)^2 + 3(1x + 3) - 5) - 3), g(x) = 1|(-1e^(-2x) + 3) + 3| + 1, x = -1.0, and x = -0.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{... | 0.1 | MATH_EXPLORATIVE |
algebra_func_area_train_0783 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = (2(3cos(1π(-4(3|x + 1| + 1)^2 + 2(3|x + 1| + 1) - 1) + 1)) - 2)/(2(3cos(1π(-4(3|x + 1| + 1)^2 + 2(3|x + 1| + 1) - 1) + 1)) - 1) and g(x) = 2|(2sin(3π(-4x^2 + 5x + 1) - 1) - 2) + 2| - 2 between the vertical lines ... | 0.2 | MATH_EXPLORATIVE |
algebra_func_area_train_0784 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = 3cos(2π(1(-3x - 2)^2 - 1(-3x - 2) - 4) + 2) + 1, g(x) = 2(-1|x|)^2 - 2(-1|x|) - 5, x = -1.5, and x = -1.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.2 | MATH_EXPLORATIVE |
algebra_func_area_train_0785 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = (1(5(-1|x| + 1)^2 - 2(-1|x| + 1) - 2) - 1)/(3(5(-1|x| + 1)^2 - 2(-1|x| + 1) - 2) + 2) and g(x) = 1|((-3x)/(-3x)) - 3| + 2 between the vertical lines x = -1.3 and x = -0.3. Round to 1 decimal place.\n\nPresent the... | 3.1 | MATH_EXPLORATIVE |
algebra_func_area_train_0786 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = (-2(2sin(1πx - 2) - 2) - 3)/(1(2sin(1πx - 2) - 2)) and g(x) = (-3x + 1)/(-1x + 2) between the vertical lines x = -4.6 and x = -3.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your an... | 3.9 | MATH_EXPLORATIVE |
algebra_func_area_train_0787 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = -2|(1((2x - 3)/(-1x - 2)) + 5) - 1| + 1 and g(x) = -1(-1cos(3πx + 2) - 2)^2 + 1(-1cos(3πx + 2) - 2) + 1 between the vertical lines x = 1.0 and x = 1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex for... | 0.5 | MATH_EXPLORATIVE |
algebra_func_area_train_0788 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = -1(5((-2x)/(-3x + 4)) + 5)^2 + 3(5((-2x)/(-3x + 4)) + 5) - 5, g(x) = -2|(-1x^2 - 5) + 1| - 3, x = 0.2, and x = 0.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 3.8 | MATH_EXPLORATIVE |
algebra_func_area_train_0789 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = 2sin(3π((-2(-1x^2 - 4) - 3)/(-1(-1x^2 - 4) - 3)) + 1) + 1 and g(x) = 2(-3|x| + 3) - 4 between the vertical lines x = 0.5 and x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your ... | 0.1 | MATH_EXPLORATIVE |
algebra_func_area_train_0790 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = -2(-5((-2x - 1)/(3x + 2)) + 3)^2 + 5(-5((-2x - 1)/(3x + 2)) + 3) - 3 and g(x) = -5(-1cos(2πx) + 3) + 5 between the vertical lines x = -0.6 and x = -0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex fo... | 1.5 | MATH_EXPLORATIVE |
algebra_func_area_train_0791 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = 2cos(2π(2|x + 3| + 2) + 2) + 3 and g(x) = (-1x - 1)/(-1x - 1) between the vertical lines x = -1.4 and x = -0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 1.0 | MATH_EXPLORATIVE |
algebra_func_area_train_0792 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = 2sin(2π((1x)/(-3x - 2)) + 3) - 1 and g(x) = -2x - 4 between the vertical lines x = -0.7 and x = -0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.2 | MATH_EXPLORATIVE |
algebra_func_area_train_0793 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1|((-3(2x + 1) + 1)/(2(2x + 1))) + 3| + 2 and g(x) = 1(-2|x + 2| - 3) between the vertical lines x = -0.5 and x = -0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
... | 5.5 | MATH_EXPLORATIVE |
algebra_func_area_train_0794 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1|(-1((1x - 3)/(1x + 2)) - 1) - 1| and g(x) = 2sin(1π(1x) - 1) + 1 between the vertical lines x = -0.5 and x = 0.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.3 | MATH_EXPLORATIVE |
algebra_func_area_train_0795 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = 3|(1sin(2πx) + 2) - 1| + 2, g(x) = 1x + 1, x = 1.9, and x = 2.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2.0 | MATH_EXPLORATIVE |
algebra_func_area_train_0796 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = (2(-1(3|(-5x^2 - 5x - 4) + 3| - 2)) + 3)/(-2(-1(3|(-5x^2 - 5x - 4) + 3| - 2)) + 3), g(x) = -3|(-2(3sin(1πx + 3) + 3)^2 + 2(3sin(1πx + 3) + 3) + 1) + 1| - 2, x = -0.6, and x = -0.4. Round your answer to 1 decimal place.\n\... | 37.2 | MATH_EXPLORATIVE |
algebra_func_area_train_0797 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1sin(1π(-5x + 4) + 2) - 3 and g(x) = (-1x + 2)/(-1x - 2) between the vertical lines x = -1.2 and x = -1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 0.0 | MATH_EXPLORATIVE |
algebra_func_area_train_0798 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = -1((-2(3|(5x^2 - 2x + 1) - 1|) - 3)/(-3(3|(5x^2 - 2x + 1) - 1|) + 1)) - 5, g(x) = (-1(4(5x^2 - 5x - 4) - 5))/(-1(4(5x^2 - 5x - 4) - 5) + 2), x = -0.7, and x = -0.0. Round your answer to 1 decimal place.\n\nPresent the ans... | 8.4 | MATH_EXPLORATIVE |
algebra_func_area_train_0799 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = -2(-4((-3x - 3)/(1x)) + 1)^2 + 4(-4((-3x - 3)/(1x)) + 1) + 4 and g(x) = -1sin(2π(-2|x - 3| - 1) + 1) - 1 from x = -1.2 to x = -0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
... | 1.5 | MATH_EXPLORATIVE |
Subsets and Splits
Unique Ground Truths Sorted
Lists unique ground truth values from the dataset, providing basic insight into the variety of possible outcomes.
Distinct Ground Truth Values Sorted
Lists unique ground truth values from the dataset, providing a basic overview of the possible outcomes.
Ground Truth Sorted Distinctly
Lists unique ground truth values from the dataset in sorted order, providing basic insight into the variety of possible outcomes.
Unique Ground Truth Values
Lists unique ground truth values from the dataset, providing basic insight into the variety of possible outcomes.