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```Function FDOUB(X As Single, Y As Single, xo As Single, yo As Single, KAPPA As Single)
' Functions for the Stream function due to elementary flows.
' This is based on equation 6.96 on page 308 in the fluids pdf
' This REAL function returns the stream function at X,Y due to a
' Doublet of strength KAPPA located at XO,YO.
Dim Pie As Single

' Assign the value of pi to the variable Pie
Pie = Application.Pi()

' Calculate the stream function due to a doublet using the given formula
FDOUB = -KAPPA * (1# / (2# * Pie)) * (Y - yo) / ((X - xo) ^ 2 + (Y - yo) ^ 2)
End Function

Function Fpsands(X As Single, Y As Single, x0 As Single, y0 As Single, hat As Single) As Single
' Functions for the Stream function due to elementary flows.

' This REAL function returns the stream function at x,y due to a
' source or a sink of strength hat located at x0,y0
' This is based on equation 6.83 on page 303 in the fluids pdf
Dim Pie As Single, A As Single, B As Single
Pie = Application.Pi()
B = X - x0
A = Y - y0
If Y > 0 Then
' The Atan2 function gives the correct answer if the y value is greater than zero,
' that is, first and second quadrants.
Fpsands = (hat / (2# * Pie)) * (Application.Atan2(B, A))
Else
' This equation corrects the atan2 problem when y is less than zero,
' that is the third and fourth quadrants
Fpsands = (hat / (2# * Pie)) * ((2# * Pie) + (Application.Atan2(B, A)))
End If

End Function

Function fvortex(X As Single, Y As Single, x0 As Single, y0 As Single, gamma As Single) As Single
' Functions for the Stream function due to elementary flows.
' This is based on equation 6.91 on page 306 in the fluids pdf.
' This REAL function returns the stream function at x,y due to a
' vortex of strength gamma located at x0,y0

Dim Pie As Single, lan As Single
Pie = Application.Pi()
fvortex = (gamma / (2# * Pie)) * Application.Ln((((X - x0) ^ 2) + _
((Y - y0) ^ 2)) ^ 0.5)

End Function

Function UniformFlowStreamFunction(X As Single, Y As Single, U As Single, alpha As Single) As Single
' Function for the stream function of uniform flow
' ? = U * (y * Cos(a) - x * Cos(a))

UniformFlowStreamFunction = U * (Y * Cos(alpha) - X * Cos(alpha))
End Function

Function SumOfResults(X As Single, Y As Single, x01 As Single, y01 As Single, KAPPA As Single, x02 As Single, y02 As Single, hat As Single, x03 As Single, y03 As Single, gamma As Single, U As Single, alpha As Single)

Dim result1 As Single
Dim result2 As Single
Dim result3 As Single
Dim result4 As Single

' Call each function and store their results
result1 = FDOUB(X, Y, x01, y01, KAPPA)
result2 = Fpsands(X, Y, x02, y02, hat)
result3 = fvortex(X, Y, x03, y03, gamma)
result4 = UniformFlowStreamFunction(X, Y, U, alpha)

SumOfResults = result1 + result2 + result3 + result4
End Function

Sub CalculateStreamFunction4()
' Specify the coordinates and parameters
Dim X As Single
Dim Y As Single
Dim U As Single
Dim alpha As Single

' Assign values to the coordinates and parameters
X = Range("D13").Value
Y = Range("E12").Value
U = Range("D6").Value
alpha = Range("D7").Value

' Calculate the stream function using the UniformFlowStreamFunction and store it
Dim result1 As Single
result4 = UniformFlowStreamFunction(X, Y, U, alpha)

End Sub

Function SumOfResults(X As Variant, Y As Variant, x01 As Single, y01 As Single, KAPPA As Single, _
x02 As Single, y02 As Single, hat As Single, x03 As Single, _
y03 As Single, gamma As Single, U As Single, alpha As Single) As Double

Dim result1 As Single
Dim result2 As Single
Dim result3 As Single
Dim result4 As Single

' Call each function for each value in X and Y arrays
Dim i As Long
For i = LBound(X, 1) To UBound(X, 1)
result1 = result1 + FDOUB(X(i, 1), Y(i, 1), x01, y01, KAPPA)
result2 = result2 + Fpsands(X(i, 1), Y(i, 1), x02, y02, hat)
result3 = result3 + fvortex(X(i, 1), Y(i, 1), x03, y03, gamma)
result4 = result4 + UniformFlowStreamFunction(X(i, 1), Y(i, 1), U, alpha)
Next i

' Sum up the results
SumOfResults = result1 + result2 + result3 + result4

'Function SumOfResults(X As Single, Y As Single, x01 As Single, y01 As Single, KAPPA As Single, x02 As Single, y02 As Single, hat As Single, x03 As Single, _
'y03 As Single, gamma As Single, U As Single, alpha As Single)

'Dim result1 As Single
'Dim result2 As Single
'Dim result3 As Single
'Dim result4 As Single

' Call each function and store their results
'result1 = FDOUB(X, Y, x01, y01, KAPPA)
'result2 = Fpsands(X, Y, x02, y02, hat)
'result3 = fvortex(X, Y, x03, y03, gamma)
'result4 = UniformFlowStreamFunction(X, Y, U, alpha)

'SumOfResults = result1 + result2 + result3 + result4
'End Function
End Function

Sub CalculateAndPlaceResult()

'Variables for FDOUB
Dim X as Single
Dim Y as Single
Dim x01 As Single
Dim y01 As Single
Dim KAPPA As Single

'Variables for Fpsands
Dim x02 As Single
Dim y02 As Single
Dim hat As Single

'Variables for fvortex
Dim x03 As Single
Dim y03 As Single
Dim gamma As Single

'Variables for UniformFlowStreamFunction
Dim U As Single
Dim alpha As Single

'Assign Values to each variable
X = Range("D13:D38").Value
Y = Range("E12:O12").Value

'FDOUB
x01 = Range("J7").Value
y01 = Range("J8").Value
KAPPA = Range("J6").Value

'Fpsands
x02 = Range("F7").Value
y02 = Range("F8").Value
hat = Range("F6").Value

'fvortex
x03 = Range("L7").Value
y03 = Range("L8").Value
gamma = Range("L6").Value

'UniformFlowStreamFunction
U = Range("D6").Value
alpha = Range("D7").Value
For I = X To 1 Step -1
For J = Y To 1 Step -1
Cells(J+12,I+4).value = SumOfResults(I, J, x01, y01, KAPPA, x02, y02, hat, x03, y03, gamma, U, alpha)
End Sub
```