def integral_approximation(function, divisions, interval):
    delta = (interval[1] - interval[0]) / divisions

    maximum = 0.0
    minimum = 0.0

    x0 = interval[0]

    for i in range(0, divisions):
        x1 = x0 + delta

        y0 = function(x0) * delta
        y1 = function(x1) * delta

        maximum += max(y0, y1)
        minimum += min(y0, y1)

        x0 = x1

    average = (maximum + minimum) / 2

    print("maximum: %s minimum: %s average: %s" % (maximum, minimum, average))


def f(x):
    return (x - 4) * (x + 8) * (x - 50) * (x - 37) * 0.0001


def test():
    integral_approximation(f, 1200, [3, 4])