#include <stdio.h>
#include <math.h>

//#define N 4
//double w[N]={0.25,0.75,0.75,0.25};
//double x[N]={-1,-1.0/3,1.0/3,1};
#define N 5
//double w[N]={7.0/45,32.0/45,4.0/15,
//             32.0/45,7.0/45};
//double x[N]={-1,-0.5,0,0.5,1};

double w[N]={.23692688505618908753, .47862867049936646802, 
 .56888888888888888891, .47862867049936646802,
 .23692688505618908753};
double x[N]={-.90617984593866399279,
   -.53846931010568309104, 0,
   .53846931010568309104, .90617984593866399279};
double g(double x){
//    return 1/(1+x*x);
    return sqrt(x);
}
double coats(double a,double delta){
    double s=0.0;
    for(int k=0;k<N;k++){
        s+=w[k]*g((x[k]+1)*delta/2+a);
    }
    return s*delta/2;
}
double ncquad(int m,double a,double b){
    double s=0.0,delta=(b-a)/m;
    for(int j=0;j<m;j++){
        s+=coats(a+j*delta,delta);
    }
    return s;
}
int main(){
    int m=1;
    for(int i=0;i<20;i++){        
        m*=2;
        double y=ncquad(m,1,3);
//        double err=fabs(y-atan(3));
        double err=fabs(y-2.0/3*(pow(3,3.0/2)-1));
        printf("%d %21.14e %g\n",m,y,err);
    }
    return 0;
}