$1.$ Write a C$++$ program that does the following:

a$.$ Create a C$++$ file with the name problem$3.$cpp$.$

b$.$ Prompt the user to enter an integer from the range $1$ to $20,$ validating the input until the user enters a correct integer. If the user fails to input a correct integer after $10$ attempts, the program chooses $10$ as the user's integer.

c$.$ Print the cube of the user's integer.

Sample run of the program:

Enter an integer between $1$ and $20$: $100$

Out of range. Enter an integer between $1$ and $20$: $-1$

Out of range. Enter an integer between $1$ and $20$: $5$

The cube of your integer is $125.$

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