I don't really understand your notation or exactly what you want. Perhaps you could clarify for this simple example, for which the entropy (as I understand it) is easily calculated.
 

Download entropy.mw

Not sure what is going on, but this gets the right form from rsolve.
 

Download rsolve.mw

Within a procedure, _npassed tells how many arguments were passed to it, and _passed gives the sequence of arguments. For example to make a procedure that takes the mean of some numbers you can use

f:=()->add(_passed)/_npassed;

Then f(1,3,5) returns 3.

In Maple 18, these were probably nargs and args, so perhaps

f:=()->add(i,i in args)/nargs;

You probably want the VIEW part, which you can extract as follows:
 

Download view.mw

Not very clear what you want. I think you want to find where the zero entries are and then replace them. Here is one way to do that; you will need to convert your older array to Array with convert(dumX,Array) first.

Or perhaps you want the sum of the numeric values.

[worksheet not displaying properly right now]

Array.mw

You can use sprintf to format a number into a string, with control over the number of decimal places etc. Here are some examples:

Download sprintf.mw

It would help if there are some initial/boundary conditions, and perhaps h(t). Maple 2015 gives:
 

Download system.mw

Your Excel file now has data at each grid point, so perhaps surfdata gives what you want?
 

Download Yasi.mw

Here is the nearest I can think of.

F:=proc(v::string,k)
   local F1,F2;
   uses DocumentTools:-Layout;
   F1:=Font(cat(v,"]"),color=blue):
   F2:=Font(sprintf(" is %g",k),color=red):
   DocumentTools:-InsertContent(Worksheet(Group(Input(Textfield(F1,F2))))):
end proc:

F("1:1",4) 

produces  "1:1] is 4" in a new input group.

Download Colortext.mw

You ask for op(1,eq5), which is the left-hand side of:

You did not indicate phi(x), just phi, so (the inner) differentiaton wrt xi gives zero (phi does not depend on xi). The same thing happens with the outer differentiation. So value on this gives zero. 

If I understand correctly, you want to find values of A[0] etc that make it zero. Here is how to equate the coefficients to find equations to be solved.

Download test1.mw

Here is one way. The theta initial condition may not be the one you want, your versions keep changing. Really it should be non-dimensionalized first. Theta=theta/thetab and Z=z/d are obvious, but the scale of v or the timescale weren't obvious to me.

Edit: looks like v might be identically zero.
 

Download DQ.mw

Since the system is linear for the variables you want to solve for (for a given t), you can use LinearSolve.

Download SoalNewton.mw

It is not very clear what information you want to show, or what form you have the data in. There are two sets of data in the table, but only one set of heights in the image, and those heights are larger than the values in the table. The lines in between the points do not seem to mean anything. The grid of x1, x2 values is not complete - are heights for missing values to be set to zero?

If only the heights in one column, say the first one, are of interest, then you could use plot with style=point (or pointplot) to plot the heights at the various x1,x2 points.

Download plot.mw

To find which value(s) of f(x) make the equation a*f(x)=0 the same on both sides, use solve:
solve(a*f(x) = 0, f(x)) assuming a>0

gives 0 for f(x). Simplify will simplify each side of the equation separately, but does not know that you want to find f(x).