Split at the crossings

You will write three functions that explain why a region must be split where the curves cross. The checker uses the curves $y = x^3$ and $y = 4x$, which cross three times.

The idea. A signed integral of $g - f$ lets a lobe below the other curve count as negative, so lobes can cancel. Making every strip positive with abs gives the true area. Each crossing shows up as a change of sign of $f - g$.

Your tasks.

1. Finish signed_area(f, g, a, b). Add 4000 strips of height g(x) - f(x), using the middle of each strip.
2. Finish total_area(f, g, a, b). Do the same, but take the absolute value of each strip height.
3. Finish count_crossings(f, g, a, b). Count how many times the sign of f(x) - g(x) changes from one strip to the next.