import math
def f(x):
    return math.sqrt(1 + x**2)
    
def petits_rectangles(n):
    s = 0
    for k in range(n):
        s = s + f(k/n) * (1/n)
    return s

def grands_rectangles(n):
    s = 0
    for k in range(n):
        s = s + f((k+1)/n) * (1/n)
    return s
valeur=10000
print(petits_rectangles(valeur))
print(grands_rectangles(valeur))

import math
def g(x):
    return 1 / (1 + x**2)
def petits(n):
    s = 0
    debut = 1
    largeur = (2 - 1) / n  
    for k in range(n):
        x = debut + (k + 1) * largeur
        s = s + g(x) * largeur
    return s

def grands(n):
    s = 0
    debut = 1
    largeur = (2 - 1) / n
    for k in range(n):
        x = debut + k * largeur
        s = s + g(x) * largeur
    return s


valeur2 = 1000
print(petits(valeur2))
print(grands(valeur2))