使用辛普森复合规则计算双积分

我之前创建过这段代码来使用辛普森复合规则计算积分，现在需要修改它以评估双积分。有谁知道如何做到这一点？我将不胜感激任何帮助。

#include <iostream>
#include <cmath>
using namespace std;
float f(float x); //returns the function we are integrating
void simpsons_rule(float a, float b, int n); // Carries out Simpsons composite rule

int main()
{
    cout << "This program finds an approximation of the integral of a function under two limits using Simpsons composite rule." << endl;
    // User is introduced to program and given explanation of what it does
    float a,b;
    int n;
    cout << "Enter the lower limit " << endl;
    cin >> a;
    cout << "Enter the upper limit " << endl;
    cin >> b; // User has freedom to specify the upper and lower limits under which the function will be integrated
    cout << "Enter the number of intervals (must be an even number) " << endl; 
    do
    {
     cin >> n; // User can also choose the number of intervals
    if(n%2 == 0 && n!=0) // If an even number of intervals was entered, the program continues and simpsons rule is carried out
    {
        simpsons_rule(a,b,n);
    }
    else
    {
        cout << "Invalid number of intervals, please re-enter a value" << endl; //If an odd number of intervals was entered, the user is prompted to enter a valid number
    }
    }while(cin); // do-while loop used to ensure even number of intervals was entered
    return 0;
}
float f(float x)
{
    return(pow(x,4) - 3*pow(x,3) + pow(x,2) + x + 1); // function to be integrated
}
void simpsons_rule(float a, float b, int n)
{
    float s2 = 0;
    float s3 = 0;
    int i;
    float h = (b-a)/n; // step length is calculated
      for(i=1; i <= (n/2)-1; i++)
      {
          if((i%2) == 0) // checks if i is even
          {
            s2 = s2 + f(a+(i*h)); // Finds the sum of all the values of f(x) where x is even
          }
      }
      for(i=1; i<=(n/2); i++)
      {
         if((i%2) == 1) // checks if i is odd
         {
            s3 = s3 + f(a+2*(i*h)); // Finds the sum of all the values of f(x) where x is odd
         }
      }
    float s = (h/3)*(f(a)+ f(b) + (2*s2) + (4*s3)); // This variable contains the final approximaton of the integral
    cout << "The value of the integral under the specified limits is: " << s << endl;