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These are questions asked by AngelaRURU

I want to plot points when it =1,2,3,..,11,12 instead of a continous line displayed in the worksheet I uploaded. How to modify the function? Thank you for helping:)

Does [Length of output exceeds limit of 1000000] mean that the function couldn't be solved and I have to modify the mathematical model?
If the results are just too long to be displayed, how can I see the results?

There are dozens of indefinite integral expressions in my worksheet. Everytime I execute the entire worksheet, the cursor always rests beside one indefinite integral expreesion and Maple stays in "Evaluating...". Even 30 minutes passed, the result of the integral couldn't come out. What bothers me is that the cursor would rest beside different indefinite integral expressions. For example, I write 4 indefinite integral expressions A, B, C and D one by one. First time, the results of A, B and C come out and the cursor rests beside D with "Evaluating...". Next time, the results of A and B come out and the cursor rests beside C with "Evaluating...".

Before the indefinite integral expressions, I wrote dozens of lines of codes aiming at assigning values to variables. As I typed more and more indefinite integral expressions into the worksheet, even evaluating the codes aiming at assigning values would spend more and more time.

Does Maple evaluate the codes line by line from the top to the end of a worksheet? If it is true, why evaluating the codes before the indefinite integral expressions becomes slowly?

How to evaluate the entire worksheet without stuck in one indefinite integral expression?

How to get the approximation of definite integral if explicit integral could not be found?

If explicit integral could not be found, is there any function or method to get the approximation of a definite integral?

ptin the file I upload is a complicated expression containing θ and r. Will the accuracy of the result be affected if I use the second method in the file to calculate the definite integral?


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