帮我用c++写一个程序，功能是用Simpson公式计算定积分，并将计算结果与精确值比较

好的，下面是用C++实现Simpson公式计算定积分的程序，其中计算的函数为f(x) = x^2，积分区间为[0,1]，精确值为1/3：

#include <iostream>
#include <cmath>

using namespace std;

double f(double x) {
    return x * x;
}

double simpson(double a, double b) {
    double h = (b - a) / 2.0;
    double c = (a + b) / 2.0;
    return (f(a) + 4 * f(c) + f(b)) * h / 3.0;
}

double adaptive_simpson(double a, double b, double eps, double whole) {
    double c = (a + b) / 2.0;
    double left = simpson(a, c);
    double right = simpson(c, b);
    if (fabs(left + right - whole) <= 15 * eps) {
        return left + right + (left + right - whole) / 15.0;
    } else {
        return adaptive_simpson(a, c, eps / 2.0, left) + adaptive_simpson(c, b, eps / 2.0, right);
    }
}

int main() {
    double a = 0.0;
    double b = 1.0;
    double eps = 1e-6;
    double whole = simpson(a, b);
    double approx = adaptive_simpson(a, b, eps, whole);
    double exact = 1.0 / 3.0;
    cout << "Approximation: " << approx << endl;
    cout << "Exact value: " << exact << endl;
    cout << "Error: " << fabs(approx - exact) << endl;
    return 0;
}

程序中使用了递归的自适应Simpson公式来计算积分，通过逐步缩小区间并不断逼近精确值，最终得到了较为精确的结果。运行程序后可以看到输出的近似值、精确值和误差，即可比较计算结果和精确值的差异。