Idiom/phrase for "example picked purposefully"

For example, when one is talking about a chemistry equation and they use values one wouldn't see in real life to illustrate a point better, or give a specific example that requires extra steps that likely won't be required in the usual cases, what would they include to say this is an example that wouldn't(or less likely to) exist in real life, but it is picked as it illustrates the point better ?

A general idiom/phrase for unarbitrary as in the example was picked with care, it isn't arbitrary would work as well.

Thanks in advance.

This is often called a “contrived example”. Cambridge gives the definition of contrived as “too obviously designed to produce a particular result, and therefore not seeming to happen naturally”, and provides an example that suggests that the word has negative connotations, but in scientific and technical writing, the negative connotations simply do not exist.