Program that allows to accept only 10 integers but loops if an odd number was entered

[DeaD_EyE]

You should split your program into 2 - 3 parts.

• A function, which asks the user to input a valid integer. If the user enters something different, he should see an error message and the question should be repeated until the user has entered a valid integer. Users are humans and they fail very often. This is a kind of input validation.
  
• A function which uses the previous function 10 times to ask the user for numbers and collect those numbers in a list. This can be done with a for-loop or a list comprehension. Copy&Paste 10 Lines is counterproductive.
  
• A function or code block on module level to output the results from the previous function.
  

One trick to count conditions, which are True, can be done with the sum function.

some_values = [1, 3, 8, 9, 13, 42]

# a generator expression in a function call
even_values = sum(value % 2 == 0 for value in some_values)

# the unrolled version as a for-loop:
results = [] # <- the list contains after the for-loop True and False booleans.
for value in some_values:
    # value % 2 == 0, if this is True, it's an even number
    results.append(value % 2 == 0)

even_values2 = sum(results)

# it translates to:
# sum((False, False, True, False, False, True))

This works because a bool is a subtype of int.

0 == False
1 == True