for rita

import math
import plotly.figure_factory as ff


def pryam(f, a, b, n):
    h = (b - a) / n
    return h * sum([f(a + i * h) for i in range(0, n)]) + 0.01 * (b-a)


def simpson_rule(func, a, b, nseg):
    if nseg%2 == 1:
        nseg += 1
    dx = 1.0 * (b - a) / nseg
    sum = (func(a) + 4 * func(a + dx) + func(b))
    for i in range(1, int(nseg / 2)):
        sum += 2 * func(a + (2 * i) * dx) + 4 * func(a + (2 * i + 1) * dx)

    return sum * dx / 3 + 0.01 * (b-a)


def f(x):
    return math.cos(x) / (x + 2)


def realint():
    return 0.1989882210658063



a, b = 0.4, 1.2
eps = 10 ** -8
print("Эпсилон: ", eps)

print("Метод прямоугольников")
data = []
data.append(['N', 'eps', 'P'])
n = 2
r1 = pryam(f, a, b, n)
data.append([n, abs(realint()-r1), ""])
n *= 2
r2 = pryam(f, a, b, n)
data.append([n, abs(realint()-r2), math.log(abs(realint()-r2)/abs(realint()-r1), 2)])
while (n < 1000000):
    n *= 2
    r1 = pryam(f, a, b, n)
    data.append([n, abs(realint()-r1), math.log(abs(realint()-r1)/abs(realint()-r2), 2)])
    n *= 2
    r2 = pryam(f, a, b, n)
    data.append([n, abs(realint()-r2), math.log(abs(realint()-r2)/abs(realint()-r1), 2)])

fig = ff.create_table(data)
fig.show()

print("n = ", n)
print("Результат: ", r2)
print("---------------------------")
print("Метод симпсона")
data = []
data.append(['N', 'eps', 'P'])
n = 4
r1 = simpson_rule(f, a, b, n)
data.append([n, abs(realint()-r1), ""])
n *= 2
r2 = simpson_rule(f, a, b, n)
data.append([n, abs(realint()-r2), math.log(abs(realint()-r2)/abs(realint()-r1), 2)])
while (n<100000):
    n *= 2
    r1 = simpson_rule(f, a, b, n)
    data.append([n, abs(realint()-r1), math.log(abs(realint()-r1)/abs(realint()-r2), 2)])
    n *= 2
    r2 = simpson_rule(f, a, b, n)
    data.append([n, abs(realint()-r2), math.log(abs(realint()-r2)/abs(realint()-r1), 2)])

fig = ff.create_table(data)
fig.show()