#include<iostream>
#include<iomanip>
#include<string>
using namespace std;
#define pi 3.14159
 int m,n,p; 
double a(double theta)//theta的下標
 { double y;
   y=0;
 return y;
 }
 double b(double theta) //theta的上標
 {double  y;
y=pi;
 return  y;
 }
 double c(double fai) // 的下標
 {double z;
z=0;
 return z;
 }
 double d(double fai) // 的上標
 {
	  double z;
	 z=2*pi;
	 return z;
 }
 double f(double r,double theta,double fai) //  
 {
	 double   I;
	 I=r*sin(theta)*sin(theta)*cos(fai);
	 return I;
 }
 double g(double r,double theta) //用Simpson公式計算函數 的值
{double fai;
	double subscript; //subscript為下標，下同
subscript=c(fai);
double supscript;//subscript為上標，下同
supscript=d(fai); 
double sum,step;
step=(supscript-subscript)/(2*p); // step為步長，下同
sum=f(r,theta,subscript)+f(r,theta,supscript);
for(int i=1;i<=(2*p-1);i++)
{ double z;
z=subscript+i*step;
if(i%2)
	sum+=4*f(r,theta, fai);
else
	sum+=2*f(r,theta, fai);
}
return sum*step/3;
}
 
double h(double r) //用simpson公式計算函數 的值
{ 
	double subscript;
subscript=a(r);
double  supscript;
supscript=b(r);
double sum,step;
step=(supscript-subscript)/(2*n);
sum=g(r,subscript)+g(r,supscript);
for(int j=1;j<=(2*n-1);j++)
{double theta;
theta=subscript+j*step;
if(j%2)
	sum+=4*g(r,theta);
else
	sum+=2*g(r,theta);
}
return sum*step/3;
} 
double Simpson(double subscript, double supscript) //用Simpson公式計算函數 
{
	double sum,step;
step=(supscript-subscript)/(2*m);
sum=h(subscript)+h(supscript);
for(int k=1;k<=(2*m-1);k++)
{
	double r;
r=subscript+k*step;
if(k%2)
	sum+=4*h(r);
else
	sum+=2*h(r);
}
return sum*step/3;
}

int main()
 {int a,b;
	 cout<<"請輸入區間a，b和等分數m，n，p："<<endl;
 cin>>a>>b>>m>>n>>p;
 double I =Simpson(a,b);
 cout<<"請輸出三重積分值:"<<I <<endl;
 return 0;
 }