! Illustrating numerical integration in LINGO;
! Keywords: Integration, Definite integral, Numerical integration;

 ! Here we input some data to be used anywhere in a LINGO model;
 DATA:
   a0 = 5; 
   a1 = 12;
   a2 = 3;
   a3 = 2;
   xl = 1; 
   xu = 4;
 ENDDATA

! A procedure is a set of code we can call anywhere
 in a CALC section;
 PROCEDURE FOF:
   y = a0 + a1*x + a2*x^2 + a3*x^3;
 ENDPROCEDURE

 CALC:
 ! Compute the integral over xl <= x <= xu, 
 where the value of y as a function of x is given by the procedure FOF;
   @SET('TERSEO',2); ! Set default output level to super terse;
   yint = @INTEGRAL( FOF, x, xl, xu, y);
   @WRITE(' The integral of ',a0,' + ',a1,'*x + ',a2,'*x^2 + ',a3,'*x^3',@NEWLINE(1));
   @WRITE('over the interval ',xl,' <= x <= ',xu,', is ', yint, @NEWLINE(1));
 ENDCALC