@Ali2020 The document stated "I do not know how you achieved your resuls". As they are listed vertically they could come from a loop. That is all.

@max125 Opps.. I post my revised answer here. Makes the answer simpler.

Download 23-3-22_A1_integration.mw

@nm I would just install over it.  Only when I have a big problem do I "clean" a program out of a computer.

@dharr Oh.  I didn't realist that about view. Very simple.

@vv Yes I hit that. Couldnt fix it so I copied and pasted the answer.

@Carl Love Answer is much neater.

@dharr , @tomleslie   Thanks. I had tried Null. Forgot about the all caps.

@Carl Love That is good. My old attempt cripples the graphics on the computer.

@acer Excellent diagnosis That looks like what happened.  I will fix it during the week and let you know.

So, in this case ooes the "DirectSearch.mla" now contain the DirectSearch, RationalTrigonometry and RonanRoutines packages?

@Joe Riel  Thank you. I don't understand whay this result is returned. The screen shot shows what is in the returned location.

See attached file on what I did.  AFIK. the mla files are in different locations; based on what I could find. I gave the different folders' locations in the question. 
 

Download Find_Library.mw

@mmcdara Thank you. Very detailed.  The matrix is built of 3 projective points [x,y,z]. Well I was trying to see if the determinalt =0. That would imply the points are colinear. I was trying last night to normailse them to [x/z,y/z,1], but even that was to much. If I could that would reduce the determinant multiplication greatly. e.g 

det=a_11*(a22-a23)-a12*(a21-a23)+a13*(a21-a22)

I will check tonight and see if the z points have a common factor.

I totally understand your point about unreadable hugh expressions.

Don't know if this is another variant of the problem but the other night was trying to upload and display a document with a 3D plot and  it just wouldn't happen. 4 attempts. Eventually just gave up on displaying the document to get answer posted. How to plot this complex function? - MaplePrimes 

@acer Yes. that is true. I just left the borders turned on to highlight to bounded area. 

Edit:- I just put the document as a url link on my start page. I don't use it all the time..

   When I first entered you equations mtaylor did not work for i2(x,y). After I saved and restarted Maple to investigate and chech the help, then mtaylor worked.

i2 := (x, y) -> -1/2*I*(exp(x*I)*sin(x)/x - exp(y*I)*sin(y)/y)/(x - y);
i2 := proc (x, y) options operator, arrow; -((1/2)*I)*(exp(I*x)*\

  sin(x)/x-exp(I*y)*sin(y)/y)/(x-y) end proc



mtaylor(i2(x, y), [x, y], 6);
             1   1             1  2   1       1  2
             - + - I (x + y) - - x  - - y x - - y 
             2   3             6      6       6   

                  1    / 3    2        2    3\
                - -- I \x  + x  y + x y  + y /
                  15                          


i3_r := -I*1/2*(i2(y, z) - i2(y, x))/(z - x);
                /    /  1   /exp(I y) sin(y)   exp(I z) sin(z)\
                |    |  - I |--------------- - ---------------|
            1   |1   |  2   \       y                 z       /
i3_r := - ----- |- I |- ---------------------------------------
          z - x \2   \                   y - z                 

     1   /exp(I y) sin(y)   exp(I x) sin(x)\\\
     - I |--------------- - ---------------|||
     2   \       y                 x       /||
   + ---------------------------------------||
                      y - x                 //




mtaylor(i3_r, [x,y,z], 8);
1   1    / 3    2      2        2              2    3    2  
- - -- I \x  + x  y + x  z + x y  + x y z + x z  + y  + y  z
6   90                                                      

        2    3\   1   2   1        1        1   2   1     
   + y z  + z / - -- x  - -- y x - -- z x - -- y  - -- z y
                  30      30       30       30      30    

     1   2   1                   1   4    1     3    1   3  
   - -- z  + -- I (x + y + z) + --- x  + --- y x  + --- x  z
     30      12                 315      315        315     

      1   2  2    1   2        1   2  2    1   3      1     2  
   + --- y  x  + --- x  y z + --- x  z  + --- y  x + --- x y  z
     315         315          315         315        315       

      1       2    1     3    1   4    1     3    1   2  2
   + --- x y z  + --- x z  + --- y  + --- z y  + --- z  y 
     315          315        315      315        315      

      1   3      1   4
   + --- z  y + --- z 
     315        315   


eval( (4), [x = 0, y = 0, z = 0]);
                               1
                               -
                               6

@acer  Works. The saved the default Start.mw into a new folder for templates and theA4.mw. Then made it editable and and added a hyperlink to the A4 format. I then pointed to it under tools-options-open worksheet at startup. Yes I emptied the table. The contents were just for  demonstration. Voted up.

@acer That does what I want. I was just trying to use them as a pair of standalone procedures, that would work together. It can be difficult to precisely ask a question when not knowing the best phrasing to use. "Export" was probably not a great choice.