@Joe Riel 

"It appears as though the pending embedded component actions are executed before the response to the dialog"

I agree.

@Joe Riel Conditional around

if assigned(Actions) then ... end if;

solves the problem. However, some points are still unclear to me. You say that "Maple first tries to execute any code in the startup region. Because that is not enabled, it doesn't occur." Why is not it enabled? I have a startup code where Actions module is described.

you say: "If you do not want to allow the startup region to execute automatically..." I want to allow the startup region to execute automatically. Does AutoExecute Security Level option 'Warn once for each worksheet' disable autoexecution?

@Joe Riel

Default AutoExecute Security Level is 'Warn once for each worksheet'. At default Security Level Maple gives an error. Every 'Warn once for each region' and 'Don't warn before execution' resolves the situation but I'd like to resolve it with default settings. Is it possible?

Thank you.

@J4James 

I guess, the button component that stops calculations has a little sense as user can always press the "white hand" button. So, you solved my problem. :) Thank you.

Alex, Carl, thank you for help. The problem is solved.

Hi @J4James 

Thank you for reply. However, I asked about programming my own button component:

>?ButtonComponent;

Unfortunately

>restart;

action when clicked doesn't interrupt the calculations.

@acer 

Problem is solved. Thank you.

PS.
Sorry my ignorance in Maple Components. Tutorial ( http://www.maplesoft.com/support/help/MapleSim/view.aspx?path=DocumentTools ) explicitly mentions about DocumentTools Package needed to be loaded for manipulations with Components properties. I missed it at first.

Working program that demonstrates the solution of the problem:

probe.mw

@acer 
Works, thank you.

@Carl Love 

>In the vast majority of cases, arguments are evaluated before they are passed.

Now the behaviour of animation is clear. Thank you.

@Carl Love 

It solves the problem. But, at what point does the case of symbolic 't' appear?

map(igcd@op, lst)

works too.

@Alejandro Jakubi 

Thank you for information.

@itsme 

I mean that CAS should not be used in cases when the task can be solved by hands for a minute. Just use the Internet if your math background is insufficient.

And yes, it is definitely a bug that should be fixed.

I also noticed the speed up of Mapleprimes working in FF. Great!