ΘΕΜΑ: Κανονας Τραπεζιου

def func():
    f = lambda x: (-1 / 6.) * (x - 1) * (x + 2) * (x - 4)
    n = input('n: ')
    a = input('a: ')
    b = input('b: ')
    h = float(b - a) / n
    summary = 0
    part1 = 0.5 * h * (f(a) + f(b))
    if n > 0:
        for i in range(1, n):
            xi = a + i * h
            summary += f(xi)
    print part1 + h * summary
 
 
if __name__ == '__main__':
    func()

# -*- coding: utf-8 -*-
from __future__ import division
import sys
 
f = lambda x: (-1/6)*(x-1)*(x-2)*(x+2)*(x-4)
 
n=input('Δώσε n. Αν n = 0, τότε έξοδος: ')
if n != 0:
    a=input()
    b=input()
 
while n <> 0:
    h = (b - a) / n
    s = f(a) + f(b)
    for i in xrange(1, n):
        s += 2 * f(a + i * h)
    print "%0.3f" % (s* h / 2)
    n=input('Δώσε n. Αν n = 0, τότε έξοδος: ')
    if n <> 0:
        a=input()
        b=input()
else:
    print "Έξοδος"
    sys.exit(1)

from __future__ import division
 
# In this function you will write down your tests, i.e. you will assert that
# your code returns the correct result for the specified input
def test_simpsons_rule():
    # case 1
    f = lambda x: 2
    assert simpsons_rule(f, 0, 1, 1) == 2
    assert simpsons_rule(f, 0, 1, 10) == 2
 
    # case 2
    f = lambda x: x
    assert simpsons_rule(f, 0, 1, 1) == 0.5
    assert simpsons_rule(f, 0, 1, 10) == 0.5
 
    f = lambda x: x**2
    # ....
 
 
def simpsons_rule(f, a, b, n):
    # write down your own implementation
    pass
 
 
if __name__ == "__main__":
    test_simpsons_rule()