program main
  implicit none
  integer :: n,i,k
  real*8 :: a,b,x,trapecio,s,suma1,suma2,x2,formula1,formula2,eps,div,h

  !variables
  n=3
  a=0d8
  b=4d8


  !calculate the additions 1 a n-1 y 2 a n-2

  suma1=0d0
  suma2=0d0
  do n=3,300,2*n
   h=(b-a)/dble(n)

        do i=1,n-1,2
            x=a+dble(i)*h
            formula1= 1/(1+(x^2))
            suma1=  suma1 + formula1
        end do

        do k= 2,n-2,2
            x2=a+dble(k)*h
            formula2 =1/(1 + (x2^2)
            suma2= suma2+ formula2
        end do

     trapecio= h/3* &
     (1+ 4*suma1 + 2*suma2 + 1(1/n^2))
     div= trapecio/(trapecio/2)
            if (div < 1d-6) then
                exit
            end if

    write(*,*), trapecio
   end do
  end