How to Integrate a Series

[elliott10]

hi, I am new to coding/programming. How do I write a macro to integrate a series of n data points using an unknown function y=f(x)?
criteria includes the following:

Show a button to run your macro
Assume there are ten x/y pairs in the spreadsheet, starting with the first x value in cell A1, and
the first y value in cell B1, and the remaining data points organized vertically downward, with all
x-values in column A and y values in column B.
The x-values are equidistant (h= 1,2,....,etc I'm guessing)
All x and y values are equal or larger than zero. There are no empty spreadsheet cells or
irregular entries (letters and such) among the data set.
To approximate the integral, calculate and sum the areas of rectangles of area A=yi * deltaX
where yi is the right hand boundary of each interval bounded by two x-values (see posted
pictures of algorithm). deltaX is the distance between two adjacent x-values.
Output the value of the integral via a message box after the integration

I started with the following:

Function Unknown(x)

y = f(x)

End Function

(new module)

Option Explicit
Sub Eurler()
'This sets the integration limit from 1 to 10

xi = 0
xf = 10
h = 0.1

'This is the number of caluclations it will run

a = (xf - xi) / h





End Sub

 

[elliott10]

Sub eulerint()
  Dim xold, yold, ynew, slope, step As Single, k As Integer

  Sheets("Euler").Activate

  xold = 0
  yold = 2
  h = 1
  'k is a counter for the output row
  k = 1

  While xold < 11

    'calculate the slope at the current x-value
    slope = xold ^ 3

    'calculate the new y-value by adding the rise to the old y value
    ynew = yold + slope * h
 
    'output to Column B aka Column 2
    Cells(k, 2) = ynew
    Range("A" & k) = xold + h

    'determine New Values before executing the loop again
    k = k + 1
    yold = ynew
    xold = k + 1
  Wend
End Sub

Book1
	A	B
1	1	2
2	4	29
3	5	93
4	6	218
5	7	434
6	8	777
7	9	1289
8	10	2018
9	11	3018
Euler

Run-time error 9 ubscript out of range when I copied and pasted into a new excel document