Untitled

import math

def f(x):
    return math.exp(x) * math.cos(x)

def simpson_integration(a, b, epsilon):
    dx = b - a
    olds = 0

    oldt = 0.5 * (f(a) + f(b)) * dx
    i = 1
    while True:
        t = 0
        spacing = dx / i
        x = a + 0.5 * spacing
        for q in range(i):
            t += f(x)
            x += spacing
        t = 0.5 * (olds + t * spacing)

        s = (4 * t - oldt) / 3

        if abs(s - olds) <= epsilon:
            return s

        olds = s
        oldt = t
        i *= 2
            
a = 0
b = 1
epsilon = 0.5 * (10**(-6))
exact_integral = (math.cos(1) * math.e + math.sin(1) * math.e - 1) / 2

integral = simpson_integration(a, b, epsilon)

print("Численное значение интеграла:", integral)
print("Точное значение интеграла:", exact_integral)