This is a program to Integrate using Trapezoidal Rule. Here you can also see the plot of the Trapezoids

Trapezoidla_with_plot.py

import numpy as np
import matplotlib.pyplot as plt

original = np.pi/4
def f(x):
	return 1/(1+(x*x))
x_real = np.linspace(0,1,1000)#This and the next line are used to create a plot of the curve represented by our f(x) function.
y_real = f(x_real)

def traezoid(f,n,a=0,b=1):
    x = np.linspace(a,b,n+1)#This creates n+1 points(i.e., n lengths) on x axis which are seperated by h
    y = f(x); h = (b - a)/n #This gives y values corresponding to the x values (a,a+h,...etc)
    y_last = y[1:];y_first = y[:-1] #Using this line we get 2 arrays which contains all y values corresponding to all x values
    s = (h/2) * np.sum(y_first + y_last) #But y_last contains all values except f(a) and y_fast contains all values except f(b)
    return s, x, y
    
n = 2
print("______________________________________________")
print("N  \t Approx Integration. \t Error")
print("______________________________________________")
for i in range(4):
    s,X,Y = traezoid(f,n)
    error = original-s
    print("{0:6.0f}".format(n),"\t","{0:1.12f}".format(s),"\t ","{0:1.12e}".format(error))
    plt.subplot(2,2,i+1)#This creates 4 subplots
    plt.plot(x_real,y_real,color='Black',label='n = %s'%n)#This plots the real function
    plt.legend(loc='best')
    for k in range(n):
        xs = [X[k],X[k],X[k+1],X[k+1]]#This and It's next line gives the points to draw Trapezoids
        ys = [0,f(X[k]),f(X[k+1]),0]
        plt.fill_between(xs,ys)#This one draw the Trapezoids
    n = n*2
plt.show()