Separation by numbers

You will turn the separation method into code. The two integrals of a separable equation are found by adding thin strips, and the unknown $y$ is found by halving an interval.

The idea. For $\dfrac{dy}{dx} = f(x)g(y)$, the separated form is $\displaystyle\int_{y_0}^{y}\dfrac{dt}{g(t)} = \int_{x_0}^{x_1} f(x)\,dx$. The right side is a number. The left side grows with $y$ (when $g > 0$), so a halving search finds the $y$ that makes the two sides equal.

Your tasks.

1. Finish integral(f, a, b, n). Use $n$ strips and the height at the middle of each strip.
2. Finish left_side(g, y0, y). Return the integral of $\dfrac{1}{g(t)}$ from y0 to y.
3. Finish solve_separable(f, g, x0, y0, x1, lo, hi). Halve the interval from lo to hi sixty times. Keep the half where the two sides meet.