!     From: "COMPUTATIONAL PHYSICS, 2nd Ed" 
! 		by RH Landau, MJ Paez, and CC Bordeianu 
! 		Copyright Wiley - VCH, 2007.
! 		Electronic Materials copyright: R Landau, Oregon State Univ, 2007;
! 		MJ Paez, Univ Antioquia, 2007; and CC Bordeianu, Univ Bucharest, 2007.
! 		Supported by the US National Science Foundation
! 		
!   int - 10d.f90: Ten dimensional integration using Monte - Carlo 
      
Program int10d

  Implicit none                    
  Integer :: m = 16, k		                         ! number of trials
  Real*8 :: s, integ(16)	
	
  s = 0.
  Do k = 1, m
    call montecarlo(integ, k);
    s  = s + integ(k)  
  End Do
  write(*, *) s/m
End Program int10d

subroutine montecarlo(integ, k)
  Implicit none
  Integer :: i, j, k, max = 65536
  Real*8 :: x, y, sum, ranDom, integ(16)
  x = 0.
  y = 0.
  sum = 0.
  Do i = 1, max
    x = 0	 				                                          ! reset x
		                                                ! sum 10 x values
    Do j = 1, 10 
      x =  x + ranDom()	      
    End Do
		                                              ! square and sum up
    y = y + x*x				                                   
    sum = sum + y/i; 
  End Do
  integ(k) = sum/max
  write(*, *) k,  integ(k)
End