double precision function trapezoidal(a, b, f, n)
      double precision a, b, f, n, h, x, s
      integer i
      external f
      h = (b-a)/n

      s = 0
      x = a
      do i = 1, n-1
         x = x+h
         s = s+f(x)
      end do
      s = 0.5*(f(a) + f(b)) + s
      trapezoidal = h*s
      return
      end

      double precision function f_1(x)
      double precision x
      f_1 = 1+x
      return
      end

      double precision function f_2(x)
      double precision x
      f_2 = exp(-x*x)*log(1 + x*sin(x));
      return
      end