import math


a, A = 2.0, 3.0
b, B = math.pi / 4, math.pi / 2

n = 200
m = 200


def f(x: float, y: float):
    return 12 * y * math.sin(2 * x * y)


def main():
    h = (A - a) / (2 * n)
    k = (B - b) / (2 * m)

    t = [1] + [4, 2] * (2 * n - 2) + [4, 1]

    def _lambda(_i: int, _j: int):
        return t[i] * t[j]

    answer = 0
    for i in range(2 * n + 1):
        for j in range(2 * m + 1):
            xi = a + i * h
            yj = b + j * k
            answer += f(xi, yj) * _lambda(i, j)

    answer = h * k * answer / 9
    print(f'ANSWER: {answer}')


if __name__ == '__main__':
    main()