Local variable is not defined within the function, but it is defined outside and above it - python-3.7

Question

I havent ran into this before, if i take the code out of triangle() and put it under the while loop everything works great. if I add triangle(input_argument) it then runs but never exits the while loop even if you type a string.
...
def main():
# Defining initial conditions.
input_argument = input("Enter a number or done: ")
triangle_list = []
def triangle():
input_argument = int(input_argument)
triangle_number = (input_argument*(input_argument+1)//2)
triangle_list.append(triangle_number)
print("Your number of", input_argument, "has a triangle number of",
str(triangle_number) + ".")
input_argument = input("Enter a new number or done: ")
# Test function for input between int or anything else.
def num_test():
try:
int(input_argument)
return True
except ValueError:
return False
while num_test() is True:
triangle()
num_test()
print(triangle_list)
main()
...
EDIT:
def num_test(input_argument):
try:
int(input_argument)
return True
except ValueError:
return False
def triangle(input_argument, triangle_list):
input_argument = int(input_argument)
triangle_number = (input_argument*(input_argument+1)//2)
triangle_list.append(triangle_number)
print("Your number of", input_argument, "has a triangle number of",
str(triangle_number) + ".")
input_argument = input("Enter a new number or done: ")
return
def main():
input_argument = input("Enter a number or done: ")
triangle_list = []
while num_test(input_argument) is True:
triangle(input_argument, triangle_list)
num_test(input_argument)
print(triangle_list)
main()

Answer 1

There's a bunch of elementary mistakes here, so let's run through a fixed version instead:
def get_input():
try:
value = input('Enter a number or done:')
return int(value)
except ValueError:
return False
def triangle(input, list):
triangle_number = (input*(input+1)//2)
list.append(triangle_number)
print(f"Your number of {input} has a triangle number of {str(triangle_number)}.")
def main():
triangle_list = []
while True:
value = get_input()
if value is False:
break
triangle(value, triangle_list)
print(triangle_list)
main()
Let's start with main, which is conceptually really simple:
we set up a list,
then we fill it,
then we print it.
How do we fill it? We loop our input aggregation:
get a value from the user. That'll either be a number, or False
if it's False, immediately stop looping.
if it's not, call our triangle function, with the current value, and the list of previous values
How do we get a value from the user? We use input(), and then try to return the int-cast version of that input. If that fails, we know the input was number a number, but otherwise we just return a number: exactly what we needed.
What does our triangle function do? It takes the current value and list of previous values, calculates some number, adds the current value to the list of previous values, prints, and exits.
Also not the Python 3 version of formatted strings: don't use string concatenation if you want a string with values-from-variables (or even values-from-other-code-calls). Use formatted strings, they're great.