[template] adaptive Simpson integral

#include<iostream>
#include<cstdio>
#include<cmath>
using namespace std;
double a,b,c,d,L,R;
double f(double x)// Primitive function 
{
    
	return (c*x+d)/(a*x+b);
}
double simpson(double l,double r)// Three o'clock Simpson 
{
    
	double mid = (l+r)/2;
	return (r-l)*(f(l)+f(r)+4*f(mid))/6;
}
double integral(double l,double r,double eps)// Adaptive Simpson 
{
    
	double mid = (l+r)/2;
	double SL = simpson(l,mid),SR = simpson(mid,r),ST = simpson(l,r);
	if(fabs(ST-SL-SR)<=(eps*15))
	    return SL+SR+(SL+SR-ST)/15;
	else return integral(l,mid,eps/2)+integral(mid,r,eps/2);
}
int main()
{
    
	cin>>a>>b>>c>>d>>L>>R;
	printf("%.6lf",integral(L,R,1e-6));
	return 0;
}