# Riemann sums for f(x) on [a,b] using n subintervals.
# The user input is between the triple hashtags. You can run the 
# code by cutting and pasting into a SageMath Cell.
#
from math import *
###
def f(x):
    return abs(cos(x) - x)

n = 100   # Integer
a = 0.0   # Float
b = 2.0   # Float
###
h = float( b - a ) / n
sum1 = 0.0
sum2 = 0.0
sum3 = 0.0
x = float( a )
for i in range( n ):
    sum1 = sum1 + f( x )
    x = x + h/2
    sum2 = sum2 + f( x )
    x = x + h/2
    sum3 = sum3 + f( x )
print("Using left endpoints: ", h * sum1)
print("Using midpoints: ", h * sum2)
print("Using right endpoints: ", h * sum3)