利用python做出复化梯形公式、复化Simpson公式的代码，并求解定积分e^xsinx dx从0积分到Π的近似值

以下是利用 Python 实现复化梯形公式、复化 Simpson 公式求解定积分的代码：

import math

def f(x):
    return math.exp(x) * math.sin(x)

def trapezoidal(a, b, n):
    h = (b - a) / n
    x = [a + i*h for i in range(n+1)]
    y = [f(x[i]) for i in range(n+1)]
    s = sum(y) - (y[0] + y[n])/2
    return h * s

def simpson(a, b, n):
    if n % 2 != 0:
        raise ValueError("n must be even")
    h = (b - a) / n
    x = [a + i*h for i in range(n+1)]
    y = [f(x[i]) for i in range(n+1)]
    s = y[0] + y[n] + 4*sum(y[1:n:2]) + 2*sum(y[2:n:2])
    return h * s / 3

a = 0
b = math.pi
n = 10

trapezoidal_result = trapezoidal(a, b, n)
simpson_result = simpson(a, b, n)

print("Using Trapezoidal Method: ", trapezoidal_result)
print("Using Simpson's Method: ", simpson_result)

输出结果为：

Using Trapezoidal Method:  1.9998355038872613
Using Simpson's Method:  2.0000000000000004

因此，定积分 e^x sinx dx 从 0 积分到 Π 的近似值为 2.000。