#!/usr/bin/python3

import math
import numpy as np
#import sympy as sp
#import matplotlib.pyplot as plt


def riemann(f,a,b,n):
    integral=0
    h=(b-a)/n
    x=a
    for i in range(n):
        integral = integral + h*f(a+h*(i+1/2))
    return integral


def trapezoid(f,a,b,n):
    integral=0
    h=(b-a)/n
    x=a
    for i in range(n):
        integral = integral + h*(f(a+i*h)+f(a+(i+1)*h))/2
    return integral


def simpson(f,a,b,n):
    return 0