In an exam in school, students are expected to solve problems with limited references and tools to assess their knowledge. On the other hand, in the science & professional world, there are no such limitations. We are free to use any resources available to us to solve the problems at hand.
Some flat-Earthers become annoyed every time we use some things like computer simulations and other tools to solve problems, especially when they help us prove spherical Earth. They would proclaim because they feel they can solve their own specific problem with pen and paper, they think they are more right than these “cheaters” with computers and other technology. In reality, the tools being used do not decide which one is more right. These flat-Earthers are merely unfamiliar with real-world cases beyond school.
Things like the occurrence of eclipses are trivial to calculate using computer simulations. These simulations use the spherical Earth model, and their predictions are accurate. Therefore, they are sufficient demonstration that the spherical Earth model works and is correct.
However, calculating the occurrence of an eclipse is very difficult using pen and paper. The Astronomical Algorithm book by Jan Meeus explains it in ten pages full of formulas, not including the prerequisite chapters. While not impossible, it is a tedious and error-prone process.
Some flat-Earthers demand that we do it manually. There are several problems with this kind of demand: 1. the computer simulations are enough evidence that the spherical Earth model works, 2. calculating things like an eclipse with pen and paper will take considerable time and effort, 3. flat-Earthers will still be unable to accept it anyway, and 4. flat-Earthers themselves cannot present a working model with the expected predictive power.