I am trying to use excel as a maths engine in a VB.NET application.
I have managed to get the basic functionality I desire, but in doing so
have to open an existing workbook using the following code:
Function CalculateFromEXCEL() As Single
    Dim xL As New Excel.Application()
    Dim xlWBk As Excel.Workbook()
    Dim xLWSht As New Excel.Worksheet()
    Dim range As Excel.Range

    xL.Workbooks.Open("C:\Test.xls", , False)
    xLWSht = xL.Workbooks(1).Worksheets(1)
    range = xLWSht.Range("A1", Reflection.Missing.Value)
    range = range.Resize(S.GetLength(0), 1)
    range.Value = xLArray
    Str = "AVERAGE(A1:A" & S.GetLength(0).ToString & ")"
    CalculateFromEXCEL = CSng(xL.Evaluate(Str))
             
    xL.Workbooks(1).SaveAs("C:\Test.xls")
    xL.Workbooks(1).Saved = True
    xL.Workbooks.Close()
    xL.Quit
    xL= Nothing
End Function

This doesn't seem to be too rigorous as I have to be able to predict the
existence of a suitably formatted workbook ahead of time.

I figure you must be able to avoid this problem by either instatiating a
new EXCEL Application object, assigning a valid workbook and worksheet
and then using this as the basis for calculations or running the EXCEL
application and worksheets etc as background objects.