PROGRAM example                   ! beginning of main program
! specify initial values and parameters
CALL initial(y,x,delta_x,xmax)
DO while x <= xmax
   CALL Euler(y,x,delta_x)        ! use simple Euler algorithm
   PRINT x,y
LOOP
END                               ! end of main program

SUB initial(y,x,delta_x,xmax)
    LET x = 1                     ! initial value of x
    LET y = 1                     ! initial value of y
    LET xmax = 2                  ! maximum value of x
    LET delta_x = 0.1             ! step size
    PRINT " x "," y "             ! print heading
    PRINT                         ! skip line
    PRINT x,y                     ! print initial values
END SUB

SUB Euler(y,x,delta_x)
    ! variables slope and change introduced for sake of clarity only
    LET slope = 2*x               ! slope at beginning of interval
    LET change = slope*delta_x    ! estimate of change during interval
    LET y = y + change            ! new value of y
    LET x = x + delta_x           ! value of x at end of interval
END SUB