"find the sum of the squares of the integers from 1 to mysquare, where mysquare is input by the user. be sure to check that the user enters a positive integer"

Please be aware that for the best performance, you shouldn't try to calculate the sum manually. Instead it's better to use a formula like n(n+1)(2n+1)/6, where n is the number input by the user. (this is a formula to calculate the sum of the first n squares: it's a famous formula).
But here is a program (in C) to do it manually:

#include
int sumSquares(int n) {
if(n == 0) return 0;
else if (n == 1) return 1;
else return (n*n) + sumSquares(n - 1);
}
int main() {
int mySquare;
puts("Enter mySquare");
scanf("%d", &mySquare);
if(mySquare < 0) mySquare *= -1;
// makes it positive if it was negative
printf("Sum of squares: %d", sumSquares(mySquare));
}