How do we compute integrals of functions or expressions that have units attached?
For example

The results of the integrals have the wrong units.

Download integration_with_units.mw

Let's say we have four equations and four unknowns and we use solve to find a solution.

The return value of solve is a set.

Here is an example

If we want to make the four expressions above procedures, the manual way is to basically copy the right-hand side of each expression and then write

T__1 := (R,m__1, m__2, g, I__s) -> ...

T__2 := (R,m__1, m__2, g, I__s) -> ...

a := (R,m__1, m__2, g, I__s) -> ...

alpha := (R,m__1, m__2, g, I__s) -> ...

Is there a way to do this automatically from the return value of solve?

If the return value were a list, I would use something like

T__1 := unapply(result[1], R, m__1, m__2, g, I__s)

T__2 := unapply(result[2], R, m__1, m__2, g, I__s)

a := unapply(result[3], R, m__1, m__2, g, I__s)

alpha := unapply(result[4], R, m__1, m__2, g, I__s)

But the return value is not a list.

So, in summary my quesions are

1) what, in general, is the best way to obtain the desired procedures?

2) is there a way to use the strategy I suggested if the result were a list, but for sets?

Download solveEqs.mw

When we use Maple input to define a procedure in a worksheet in Document mode, how do we evaluate/execute the command. I am used to just hitting <Enter> when using 2d Math. Today, I've been trying to use Maple input, but when I hit <Enter> nothing happens, or something does happen that messes up the definition such that I get a 

Warning, premature end of input, use <Shift> + <Enter> to avoid this message.

right in the middle of the procedure which then generates a 

Error, global declaration unexpected outside procedure or module
Error, missing operator or `;`

and the only way to even execute and see these errors is by executing the whole worksheet. 

Attached is an example: 
 

I can hit enter on the 2d math version, but not on the first 1d math version. On the 1d version, if I go to right after "end:" and hit <Enter> I get an error: Error, reserved word `end` unexpected.

Download 1dmathproc.mw

The documentation on plots:-densityplot says

Any additional arguments are interpreted as options which are specified as equations of the form option = value. For example, the option grid = [m, n] where m and n are positive integers specifies that the plot is to be constructed on an m by n grid at equally spaced points in the ranges a..b and c..d respectively. By default a 49 by 49 grid is used; thus 2401 points are generated, and 2401 colored cells are displayed.

Consider the following simple example

If we look at the output from the print statement inside of g we see

Download DensityPlotGridQuestions.mw

That is, there are 16 points in the grid, not 5x5=25.

Is the documentation incorrect or did I miss something?

This question is about an aspect of the code below. In fact, the code could be made simpler to get at the question, but I chose to show you how the problem originated. 

We start with a 4x3 matrix A. There is a procedure, convertArrayToTable, that takes this matrix and creates a table. The table is such that the keys are the numbers in the first column of A. For each such key k1, the associated value is another table. The latter table has as keys the values in the second column that have k1 in the first column.

Now, further below, if you are curious I write about why I am doing this (what the exact real problem is). For now, I am generating a matrix B which in is formed by the concatenation of A and 2A, along the column (ie, A on top of 2A).

So for this matrix B, the table T that is generated has, for example a key 1 and the associated value is a table with keys 0.2 and 0.400000000000000.

I wish to be able to access T[1][0.400000000000000] but this is not working and I don't know why.
 

Download tableDecimalIndex.mw

So now just a brief note on why I want to create such a table.

I want to create a density plot based on the values in the rows of B. In the case of the simple example shown above, the grid of values would be based on values of x from 1 to 4 and of y from 0.2 to 0.400000000000000. Then I would specify, say "grid=[5,3]" for an eight point grid. 

In this example I am assuming the points used by the densityplot procedure would be exactly the ones in the rows of B, ie (1,0.2), (2,0.2), (3,0.2), (4,0.2),(1,0.400000000000000),(2,0.400000000000000),(3,0.400000000000000),(4,0.400000000000000).

The function I would pass in the signature

densityplot(f, a..b, c..d)

would be a custom procedure that I am assuming would be called as f(x,y) and would simply look up T[x][y] in the table I created to get the value.

Of course in my real problem the grid has way more points.

I am making a lot of assumptions about this densityplot procedure, but the documentation isn't very clear at all.

Here is a proof of concept of what I am trying to achieve (note that below, I am avoiding the issue of the decimal keys in tables by using integers instead):
 

In the above output, the output from the print statement in the f procedure is not being shown. Locally on my computer it is shown and f is called at the expected values (the ones in the rows of B). So that is all good. The issue seems to always go back to keying in to tables with certain (but not all) decimal numbers

Download DensityPlot.mw