用矩形法积分近似运算(1)sin(⁡x)，下限为0.0,上限为pir/2。 (2)exp(x)，下限为0.0,上限为1.0。 (3)4.0/(1+x×x)，基类(integer)成员数据包括积分上下限b和a，分区数n，步长step= n b−a ​ ，积分值result。 定义积分函数integerate()为虚函数，它只显示提示信息。 派生的矩形法类(rectangle)重定义integerate()，下限为0.0,上限为1.0。

下面是题目要求的三个部分的代码实现：

1. sin(x)的矩形法积分近似运算：

import math

class integral:
    def __init__(self, a, b, n):
        self.a = a
        self.b = b
        self.n = n
        self.step = (b - a) / n
        self.result = 0.0

    def integrate(self):
        print("This is the base class and cannot be used to integrate.")

class rectangle(integral):
    def integrate(self):
        self.result = 0.0
        for i in range(self.n):
            x = self.a + i * self.step + self.step / 2.0
            self.result += math.sin(x) * self.step
        print("The approximate value of sin(x) integral from 0 to pi/2 is:", self.result)

# 测试代码
r = rectangle(0.0, math.pi/2, 100)
r.integrate()

2. exp(x)的矩形法积分近似运算：

import math

class integral:
    def __init__(self, a, b, n):
        self.a = a
        self.b = b
        self.n = n
        self.step = (b - a) / n
        self.result = 0.0

    def integrate(self):
        print("This is the base class and cannot be used to integrate.")

class rectangle(integral):
    def integrate(self):
        self.result = 0.0
        for i in range(self.n):
            x = self.a + i * self.step + self.step / 2.0
            self.result += math.exp(x) * self.step
        print("The approximate value of exp(x) integral from 0 to 1 is:", self.result)

# 测试代码
r = rectangle(0.0, 1.0, 100)
r.integrate()

3. 4.0/(1+x^2)的矩形法积分近似运算：

import math

class integral:
    def __init__(self, a, b, n):
        self.a = a
        self.b = b
        self.n = n
        self.step = (b - a) / n
        self.result = 0.0

    def integrate(self):
        print("This is the base class and cannot be used to integrate.")

class rectangle(integral):
    def integrate(self):
        self.result = 0.0
        for i in range(self.n):
            x = self.a + i * self.step + self.step / 2.0
            self.result += 4.0 / (1 + x * x) * self.step
        print("The approximate value of 4/(1+x^2) integral from 0 to 1 is:", self.result)

# 测试代码
r = rectangle(0.0, 1.0, 100)
r.integrate()