Q:

Tensorflow doesn't calculate summary

I try to understand how to collect summaries for tensorboard and wrote a simple code to increment x from 1 till 5.
For some unknown reason I see variable My_x as 0 in all steps.
import tensorflow as tf

tf.reset_default_graph() # To clear the defined variables/operations

# create the scalar variable
x = tf.Variable(0, name='x')

# ____step 1:____ create the scalar summary
x_summ = tf.summary.scalar(name='My_x', tensor=x)

# accumulate all summaries
merged_summary = tf.summary.merge_all()

# create the op for initializing all variables
model = tf.global_variables_initializer()

# launch the graph in a session
with tf.Session() as session:
    # ____step 2:____ creating the writer inside the session
    summary_writer = tf.summary.FileWriter('output', session.graph)

    for i in range(5):
        #initialize variables
        session.run(model)

        x = x + 1

        # ____step 3:____ evaluate the scalar summary
        merged_summary_ans, x_summ_ans, x_ans = session.run([merged_summary, x_summ, x])
        print(x_ans)
        print(x_summ_ans)
        print(merged_summary_ans)

        # ____step 4:____ add the summary to the writer (i.e. to the event file)
        summary_writer.add_summary(summary=x_summ_ans, global_step=i)

    summary_writer.flush()
    summary_writer.close()
    print('Done with writing the scalar summary')

A:

There are two problems that I can see in your code:
1) The first is that in each loop you are re-initialising the global variables again. This is resetting x back to its original value (0).
2) Second of all when you are updating x you are overwriting the link to the variable with a TensorFlow addition operation. Your code to increase x replaces 'x' with a tf.add operation and then your summary value is no longer tracing a tf.Variable but an addition operation. If you add "print(x)" after you define it and have it run once in every loop, you will see that originally it starts out as <tf.Variable 'x:0' shape=() dtype=int32_ref> but then after seeing that "x = x+1" then print(x) becomes Tensor("add:0", shape=(), dtype=int32). Here you can see that tf.summary.scalar is only compatible with the original value and you can see why it can't be updated.
Here is code I altered to get it to work so you can see the linear of the value of x in Tensorboard.
import tensorflow as tf
tf.reset_default_graph()

x = tf.Variable(0, name='x')
x_summary = tf.summary.scalar('x_', x)
init = tf.global_variables_initializer()

with tf.Session() as session:
    session.run(init)
    merged_summary_op = tf.summary.merge_all()
    summary_writer = tf.summary.FileWriter('output', session.graph)

    for i in range(5):
        print(x.eval())
        summary = session.run(merged_summary_op)
        summary_writer.add_summary(summary, i)
        session.run(tf.assign(x, x+1))

    summary_writer.flush()
    summary_writer.close()

