Untitled

import math

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

def simpson_integration(f, a, b, n):
    h = (b - a) / n
    integral = 0
    
    for i in range(n):
        x0 = a + i * h
        x1 = a + (i + 0.5) * h
        x2 = a + (i + 1) * h
        
        integral += h / 6 * (f(x0) + 4 * f(x1) + f(x2))
    
    return integral

def runge_estimation(f, a, b, n, old_integral, epsilon):
    new_integral = simpson_integration(f, a, b, n)
    error = abs(new_integral - old_integral) / 15
    
    if error < epsilon:
        return new_integral
    
    return runge_estimation(f, a, b, 2 * n, new_integral, epsilon)

a = 0
b = 1
epsilon = 0.5 * (10**(-6))
n = 1000  # количество разбиений
exact_integral = math.exp(b) * (math.sin(b) + math.cos(b)) - math.exp(a) * (math.sin(a) + math.cos(a))

integral = simpson_integration(f, a, b, n)
integral = runge_estimation(f, a, b, n, integral, epsilon)

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