This stems from the same warning-type bug that appears if you create a local variable within a procedure or module and the local variable is never used.  For example, in an .mpl document, create:

myproc := proc()    local x;   end proc;

--> Warning appears about the lack of using the variable with a garbage variable name

For your example, assign value to "a" and "c" each and the warning disappears. 

This bug has appeared for many versions. Apparently, it has not been fixed. 

Error, (in simplify/sqrt/fraction) invalid input: denom expects its 1st argument, x, to be of type {algebraic, list, set}, but received pascal

@mmcdara Regarding this bug if the type is a list or vector, it does not appear for either type for the 2022 and 2023 versions.

It is my experience that this behavior is not new. Nor do I expect it to disappear with the  2023 version. For me, the single most common problem with the GUI is the following: when I return to an already open session of Maple after the computer has been put to sleep and reawakened, the sub-menus do not open up. 

In the past, I would close Maple completely and re-open it. However, I've started using a new trick:  instead of closing everything, open another instance of the program, then perform some work within it, and somehow it solves the "lack of response" in the first instance. Try that method. 

I once asked the tech people about this "lack of response" or sub-menus failing to open. They said they know about these issues and attribute them to the Java API. But don't quote me. I may have misunderstood what they said. Hopefully, someone from Maplesoft can provide thoughts on this issue. 

I downloaded the file and opened it in Maple 2022.2 (Windows 10). !!! the file. The output is as expected, with no errors. I also redownloaded it and executed it one "enter command" at a time. No problems. The errors disappeared. Finally, I entered some additional commands using the Expressions Palette. Again, it worked as expected. This leads me to the following questions - which version are you using and under which OS?  

I worked with 40 students this past semester. Maple 2022.1 in the Mac OS led to a slew of weird Maple interface issues, though I don't remember any like this. Major problems that occurred were having an execution group not generating an output, and since we used worksheet mode, the enter key did not process a command in an execution group. Oddly, the fix was using the !!! button. The update to 2022.2 fixed a number of problems like this. 

I'm a big fan of the 2d-math. It sells, and it lowers the activation barrier in learning how to use Maple. However, it is my experience that the document mode should best be employed only by long-time users of Maple. By separating executable groups from text groups, the worksheet mode better labels "text" and "non-executable math" from "executable math," which means fewer misunderstandings of what the Maple document is doing. 

Download DataFrames_question.mw

@PaulNewton

Given what you wrote above, the only other option that I can think of is the stop button on the menu bar.

@Carl Love 

Thank you for your highly informative and well-written post. As someone attempts to teach basic Maple usage to students, I will continue to refer to your work here. The Programming Manual heavily emphasizes the word "name" rather than "symbol". The word "symbol" appears precisely only twice in chapter 1 and once in chapter 2.

Decades ago when I first became aware of Maple, there was heavy use of the catenated variables. But then it fell into disfavor. Given that they are always global, I understand why now. I don't remember reading this information in the Programming Manual. Nor do I understand why the authors of Maple would adopt this policy. Regardless, major upvote.

Note, I tried to email you directly, but Google rejected my academic address. 

@zenterix 

Download Context_Panel.mw

Download Non_executable_math.mw

Both systems have their benefits. However, there is one fomat that is popular with those who read Maple which I interpret as the worksheet-document hybrid.

Write everything in a worksheet mode.  Then when ready to share with others, either hit F9 or deselect the option under View --> Show/Hide Contents --> Execution Group Boundaries

Without the execution and text group boundaries, the "document" has much of the appearance of a document but still with the structure of a worksheet.  

A small request. Any chance you folks can add information about Physics:-Version() to help, and to make reference to it in the Physics Overview section?

@jschatzman Refering to A), like many other computing languages, the Maple language is case sensitive. Hence pi does not equal Pi. 

Pi is the defined constant. pi is a variable. (Another example is the variable "e" and "e" which equals exp(-1).) However, when Maple displays either, it appears as the Greek letter, i.e, it appear the same. (There has been requests to have the defined constant displayed in a different color. However, since I suspect so few people use the variable pi, more folks would be annoyed by the change in color.) 

If you use Common Symbols palette, Pi is distinct from the pi character in Greek palette.  

For the defined constants, you can go to this webpage:  https://www.maplesoft.com/support/help/errors/view.aspx?path=initialconstants

@Rouben Rostamian  Again, with this newer worksheet, no black image appears in Windows 10. 

The only reason I mention the graphics board / video setup is because I have an even weirder problem. When I have Maple open and I turn off the primary monitor (Dell 34"), Maple quits. No other app / program quits. This occurs both in 2021 and 2022.  I'm not even sure how to report it as a bug. 

..but when I open the worksheet, the tubes are red and red. I'm using exactly the same version of Maple 2022.1 that you are. 

Re-executing the worksheet also produces red and red. 

I don't know what graphics card my Dell (Windows 10) laptop is using.