How to determine the function of this "black-box"?

Question

Imagine a black box which accepts a digital input signal which is a pure sine wave and outputs the area between this input signal and some constant data set over a sample window.

Given the input and output signals, is it possible to determine the sample data set?

Edit: Here is how the box calculates area between two data points...

    private double areaBetween(double a, double b)
    {
        if (Math.Sign(a) == Math.Sign(b))
        {
            if (Math.Abs(a) > Math.Abs(b))
                return a - b;
            else
                return b - a;
        }
        else
        {
            return a + b;
        }
    }

Answer 1

Since integrals are additive, your output is really just the integral of the green input signal over the sample window, minus the integral of the blue sample signal over the same sample window.

The blue integral is constant, and is the only way the sample signal influences your output. So all you can learn about the blue signal from observing the black-box relation between the green and red signals is what the average value of the blue signal is -- that is, in this case, $0$.

(On the other hand, this is also all you need to reconstruct the behavior of the black box for a different input signal, if that is what you're ultimately interested in).