Calculator that can add/subtract/divide/multiply two inputs
Immutable sequences
operators should be a tuple (i.e. ('+', ...)), since you don't change it.
Nested functions
instructions should be moved to the global level - you shouldn't need a closure, and should be passing information between instructions and run_calculator with parameters and return values, not closure variables.
Index-based selection
It's a little awkward to ask that the user select an operator based on numerical index. Make operators a dictionary instead, and have the user input the operator character. Of course, this is only possible if the parameters of your homework assignment permit.
Never except: 
Seriously. except ValueError: instead. Otherwise, you'll catch exceptions you don't want to, including user-break Ctrl+C.
Parens
Python doesn't need parens here:
while (True):

so delete them.
Logic inversion
    if restart.lower() == 'y':
        continue
    else:
        print(&quot;Results:&quot;)
        for x in range(len(answers)):
            print(f&quot;{answers[x]}&quot;)
        break

is more easily expressed as
    if restart.lower() != 'y':
        print(&quot;Results:&quot;)
        for x in range(len(answers)):
            print(f&quot;{answers[x]}&quot;)
        break