' version 17-09-2015
' compile with: fbc -s console

#Define screen_width 1024
#Define screen_height 256
ScreenRes screen_width, screen_height, 8
Width screen_width\8, screen_height\16

Function f1(x As Double) As Double
    Return x^3
End Function

Function f2(x As Double) As Double
    Return 1/x
End Function

Function f3(x As Double) As Double
    Return x
End Function

Function leftrect(a As Double, b As Double, n As Double, _
ByVal f As Function (ByVal As Double) As Double) As Double

    Dim As Double sum, x = a, h = (b - a) / n

    For i As UInteger = 1 To n
        sum = sum + h * f(x)
        x = x + h
    Next

    leftrect = sum
End Function

Function rightrect(a As Double, b As Double, n As Double, _
ByVal f As Function (ByVal As Double) As Double) As Double

    Dim As Double sum, x = a, h = (b - a) / n

    For i As UInteger = 1 To n
        x = x + h
        sum = sum + h * f(x)
    Next

    rightrect = sum
End Function

Function midrect(a As Double, b As Double, n As Double, _
ByVal f As Function (ByVal As Double) As Double) As Double

    Dim As Double sum, h = (b - a) / n, x = a + h / 2

    For i As UInteger = 1 To n
        sum = sum + h * f(x)
        x = x + h
    Next

    midrect = sum
End Function

Function trap(a As Double, b As Double, n As Double, _
ByVal f As Function (ByVal As Double) As Double) As Double

    Dim As Double x = a, h = (b - a) / n
    Dim As Double sum = h * (f(a) + f(b)) / 2

    For i As UInteger = 1 To n -1
        x = x + h
        sum = sum + h * f(x)
    Next

    trap = sum
End Function

Function simpson(a As Double, b As Double, n As Double, _
ByVal f As Function (ByVal As Double) As Double) As Double

    Dim As UInteger i
    Dim As Double sum1, sum2
    Dim As Double h = (b - a) / n

    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

' ------=< main >=------

Dim As Double y
Dim As String frmt = " ##.##########"

Print
Print "function     range       steps  leftrect      midrect       " + _
                              "rightrect     trap          simpson "

Print "f(x) = x^3   0 - 1         100";
Print Using frmt; leftrect(0, 1, 100, @f1); midrect(0, 1, 100, @f1); _
rightrect(0, 1, 100, @f1); trap(0, 1, 100, @f1); simpson(0, 1, 100, @f1)

Print "f(x) = 1/x   1 - 100      1000";
Print Using frmt; leftrect(1, 100, 1000, @f2); midrect(1, 100, 1000, @f2); _
                    rightrect(1, 100, 1000, @f2); trap(1, 100, 1000, @f2); _
                    simpson(1, 100, 1000, @f2)

frmt = " #########.###"
Print "f(x) = x     0 - 5000  5000000";
Print Using frmt; leftrect(0, 5000, 5000000, @f3); midrect(0, 5000, 5000000, @f3); _
                    rightrect(0, 5000, 5000000, @f3); trap(0, 5000, 5000000, @f3); _
                    simpson(0, 5000, 5000000, @f3)

Print "f(x) = x     0 - 6000  6000000";
Print Using frmt; leftrect(0, 6000, 6000000, @f3); midrect(0, 6000, 6000000, @f3); _
                    rightrect(0, 6000, 6000000, @f3); trap(0, 6000, 6000000, @f3); _
                    simpson(0, 6000, 6000000, @f3)

' empty keyboard buffer
While InKey <> "" : Wend
Print : Print "hit any key to end program"
Sleep
End