program simpson
   implicit none
   double precision,parameter::a=-1.0d0,b=1.0d0
   double precision f,x
   integer i,n
   double precision ii,xi,yi,y0,yn,h

   f(x)=8.0d0/3.0d0*(1.0d0-x*x)**1.5d0

   write(*,*) 'input num of partitions'
   read(*,*) n
   if(mod(n,2)/=0)then
      write(*,*) 'error!'
      stop
   end if
   y0=f(a)
   yn=f(b)
   ii=y0+yn
   h=dabs(b-a)/dble(n)
   do i=1,n-1
      xi=a+dble(i)*h
      yi=f(xi)
      if(mod(i,2)==0)then
         ii=ii+2.0d0*yi
      else
         ii=ii+4.0d0*yi
      end if
   end do
   ii=ii*h/3.0d0
   write(*,100) ii
   100 format(1x,'I=',f20.13)
   stop
   end