import math
def fun(x):
    return x+math.sin(2**x) # in python need ** instead ^
from scipy.integrate import quad
a=-1
b=2
intV,errV = quad(fun,a,b) # first element is integral estimate, second element is
# an estimate of an upper bound on the error
# intV = quad(fun,a,b)[0]
# errV = quad(fun,a,b)[1]
#print(intV)
N=[2,4,8,16,32,64]
left = []
right = []
trap = []
simp = []
exact = [intV for n in N]
for n in N:
    h = (b-a)/n
    x = [a+j*h for j in range(n+1)]
    y = [fun(bubba) for bubba in x]
    left += [h*sum(y[:-1])] # y[:-1] means all indices up through the 2nd last index
    # y[A:B] means indices A through B-1.
    right += [h*sum(y[1:])]
    trap += [h/2*(y[0]+y[-1]+2*sum(y[1:-1]))] # note y[1:-1]=y[1:n]
    simp += [h/3*(y[0]+y[-1]+4*sum(y[1:-1:2])+2*sum(y[2:-1:2]))]
    #y[1:-1:2] means indices 1,3,5,...,stop before the last #
#print(n,left,right,trap,simp,intV)
# to make a nice chart, I will make a data frame
import pandas as pd
dict = {'n':N,'left':left,'right':right,'trap':trap,'simp':simp,'exact':exact}
# The above is called a 'dictionary'
df = pd.DataFrame(data=dict)
print(df) # prints nice table