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Graphical and numerical integration with Riemann sums. Left, center, right, and trapezoid.

from math import *
from matplotlib.pyplot import *

#Define the function to integrate 
def f(x): return x**2

def run():
  print("Plot Parameters")
  print("----------------------")
  a = float(input('xmin= '))
  b = float(input('xmax= '))
  c = float(input('ymin= '))
  d = float(input('ymax= '))

  print()
  print("Integration Parameters")
  print("----------------------")
  print("Type: 1: Left")
  print("      2: Center")
  print("      3: Right")
  print("      4: Trapezoid")
  print()
  t = input("Type: ")
  if (t == "1") or (t == "4"):
    r=0
  elif t == "2":
    r=1
  else:
    r=0.5

  xa = float(input('a= '))
  xb = float(input('b= '))
  n = int(input('n= '))

  dx = (xb-xa)/n

  x = [a+i*(b-a)/50 for i in range(51)]
  y = [f(i) for i in x]

  if t == "4":
    area = (f(xa)+f(xb)+2*sum(f(xa+i*dx) for i in range(1,n)))*dx/2
  
  else:
    xs = [xa+(i+r)*dx for i in range(n)]
    ys = [f(i) for i in xs]
    area = sum(ys)*dx

  text(a,d,"  Area= "+str(area))

  axis((a,b,c,d))
  plot(x,y,'blue')
  grid()


  if t == "4":
    for i in range(n):
      plot((i*dx+xa,i*dx+xa,(i+1)*dx+xa,(i+1)*dx+xa),(0,f(i*dx+xa),f((i+1)*dx+xa),0),'red')
 
  else:
    for i in range(n):
      plot((i*dx+xa,i*dx+xa,(i+1)*dx+xa,(i+1)*dx+xa),(0,f((i+r)*dx+xa),f((i+r)*dx+xa),0),'red')
  show()