How do I add an expression if it's a string?

Question

I'm trying to write a calculator program that has the features of addition, subtraction, and the notation X^ which means X^2. I'm completely lost and I don't know what to do. This is the code I have so far and an example of an expression I'm trying to solve.

1000 + 6^ - 5^ + 1;

and my code is

#include <iostream>
using namespace std;

int main()
{
    int sum;
    char answer, num, sign, add = '+', minus = '-';
    cin >> answer;
    string str;
    str += answer;

    while (cin >> sign)
    {
        if (sign == '^')
        {
            str += add + answer;
        }
        else if (sign == '+')
            {
                cin >> num >> sign;
                if ((cin >> sign) == '^')
                {
                    str += add + num + add + num;
                }
                else
                {
                    str += add + num;
                }
            }
            else if (sign == '-')
            {
                cin >> num >> sign;
                if ((cin >> sign) == '^')
                {
                    str += minus + num + minus + num;
                }
                else
                {
                    str += minus + num;
                }
            }
            else if (sign == ";")
            {
                for(int i = 0; i < str.length(); i++)
                {
                    int digit = str[i] - 48;

                }
            }
    }

    return 0;
}