FUNCTION leftRect(a, b, n)
     h = (b - a) / n
     sum = 0
     FOR x = a TO b - h STEP h
        sum = sum + h * (f(x))
     NEXT x
     leftRect = sum
END FUNCTION

FUNCTION rightRect(a, b, n)
     h = (b - a) / n
     sum = 0
     FOR x = a + h TO b STEP h
        sum = sum + h * (f(x))
     NEXT x
     rightRect = sum
END FUNCTION

FUNCTION midRect(a, b, n)
     h = (b - a) / n
     sum = 0
     FOR x = a + h / 2 TO b - h / 2 STEP h
        sum = sum + h * (f(x))
     NEXT x
     midRect = sum
END FUNCTION

FUNCTION trap(a, b, n)
     h = (b - a) / n
     sum = f(a) + f(b)
     FOR i = 1 TO n-1
        sum = sum + 2 * f((a + i * h))
     NEXT i
     trap = h / 2 * sum
END FUNCTION

FUNCTION simpson(a, b, n)
     h = (b - a) / n
     sum1 = 0
     sum2 = 0

     FOR i = 0 TO n-1
        sum1 = sum1 + f(a + h * i + h / 2)
     NEXT i

     FOR i = 1 TO n - 1
        sum2 = sum2 + f(a + h * i)
     NEXT i

     simpson = h / 6 * (f(a) + f(b) + 4 * sum1 + 2 * sum2)
END FUNCTION