Question: limit of numerically calculated function & plot of procedure

There are two questions:

1. I have an ODE system solved numerically, but it has a singularity at Pi because of cot(x). I need to know whether the solution goes to infinity at this point or it has some value. I tried the limit operation, but it doesn't seem to work. Am I doing it wrong or is there no way to do such thing? See details in file 1 1.mw.

I know I can evaluate the function at point Pi - 10^(-10), Pi - 10^(-9) etc, and it has really close values there, but still I doubt it is a strong proof of the function not going to infinity.

Also the following "technical" question: why is Maple building the plot from 0 to Pi (or from -Pi to Pi symmetrically), even if I enter different range? For cot(x) it builds the plot normally, not just from -Pi to Pi, althouth cot(x) has singularity at Pi AND at 0, but my plots are somehow broken off at Pi.

2. I have 2 similar procedures and I need the plots of both of them. But first plot is built correctly and for the second there appears an error: "Error, (in plot) procedure expected, as range contains no plotting variable". I tried entering other ranges, including very small ones, but it didn't help. It calculates the values at points of range nicely though. See details in file 2 2.mw.

And one more time "technical" question about warnings in the procedures. I tried typing "local" or "global" before variables, but Maple gives me an error. How do I get rid of the warnings correctly?

I know it is difficult to see into those problems, but I strongly look for help! Thank you for your time!