I would like to calculate a definite integral in the attached file. Doing so numerically is straightforward. However, a symbolic approach initially fails due to three points of discontinuity in the integrand. Yet, these points can be remedied by taking limits. How can the domain in Maple be extended using these limits to achieve continuity across the entire domain?

testint.mw

I would like to solve a differential equation using a series expansion in the attached file for practice purposes. How can the number of terms in the series solution be adjusted? I couldn't find anything about this in the help text.
BTW:
The differential equation is exceptionally tricky for a symbolic solution ;-) .

testdgl-1.mw

In the attached file, I have solved an ordinary differential equation implicitly. The simplification that is obviously possible using "simplify" is not being performed. Furthermore, "implicitplot" is not working either. I would appreciate some advice.

test.mw

As an exercise to further familiarize myself with Maple, I would like to calculate the definite integral specified in the attached file. The integrand has an antiderivative, and a source lists the value of the integral as approximately 0.57... Based on the plot, this value is plausible according to a simple estimate (Pi/2 * 0.8 / 2). Following standard practice taught in school, I therefore calculated the difference between the values ​​of the antiderivative at the limits of integration. Surprisingly, the result is a complex number. What am I doing wrong? Did the internal Maple calculation switch to complex principal values?

testint5.mw

For the purpose of practicing with Maple, I have worked on a definite integral in the attached file. I found it on the Internet. According to a side calculation, it can only be calculated using famous special functions or series expansions. That is why I am only interested in the numerical evaluation here. According to auxiliary calculations, it can only be computed using famous special functions or a series expansion. It is known that the series expansion of the antiderivative converges very rapidly. Therefore, for comparison purposes, I calculated the values ​​for integration limits of 10 and 100 instead of infinity. In the first graph, the two result curves appear to coincide perfectly. Is there a way to zoom in locally - like using a magnifying glass - to make the difference in the ordinate values ​​visible?

Download testint3.mw