Accessing returned values from a function, by another function

You're pretty much there. You can remove all globals, then just store the values returned from each function to local variables, and pass them in to new functions.

The only other changes I've made below are:

• Breaking out of the evaluation loop if the answer is guessed correctly.
• Printing a message if no guess is found in the given time. See: Else clause on Python while statement
• The bottom two lines allow the script to be run from the command line. See: What does if __name__ == "__main__": do?

Otherwise you're looking good.

import random

def main(): # main function
    print("Welcome to the number guesser game")
    lower, upper, rand = range_func()
    total_guesses = max_guess_number(lower, upper)
    evaluation(rand, total_guesses)

def range_func():   # allows user to select a range for the number guess
    print("Please select a range in which you would like to guess.")
    lower_range_cut = int(input("Lower boundary limit: "))
    upper_range_cut = int(input("Upper boundary limit: "))
    random_number = random.randint(lower_range_cut, upper_range_cut)
    return lower_range_cut, upper_range_cut, random_number

def max_guess_number(low,high): # returns the total number of guesses
    total_numbers = (high - low) + 1
    total_guesses = 0
    while (2**total_guesses) < total_numbers:
        total_guesses += 1
    print ("You have a total of %d guesses\n"
           "for your range between %d to %d"
           % (total_guesses, low, high))

    return total_guesses

def evaluation(random_number, total_guesses): # evaluates the users input
    guess_count = 0
    while guess_count < total_guesses:
        guess_count += 1
        user_guess = int(input("Your guess: "))
        print("Your guess is: %d" % (user_guess))
        if (random_number == user_guess):
            print("You got it!")
            break
    else:
        print "Sorry, you didn't guess it in time. The answer was: %d" % random_number

if __name__ == '__main__':
    main()

You don't need to define global. You can just assign the values you are returning from a function to variable(s).

A simple example:

def add(a, b):
    """This function returns the sum of two numbers"""
    return a + b

Now in your console, you could do following

# print the return
>>> print(add(2, 3))
5

# assign it to a variable
>>> c = add(2, 3)
>>> c
5

In your main function you need to assign the values which are returned by different functions to variables which you can further pass to other functions.

def main(): # main function
    print("Welcome to the number guesser game")
    lower_range_cut, upper_range_cut, random_number = range_func()
    total_guesses = max_guess_number(lower_range_cut, upper_range_cut)
    evaluation(random_number, total_guesses)