what calculator should I buy?
Casio CP400
Casio cg500
texas instruments ti-nspire cx cas
hp prime

I study mechatronic engineering
Kinda depends where you live.

The Casio cp400 and cg500 are the same calculator as far as I know, the cg500 is the North American version while the cp400 is sold in Europe. That calculator is really cool, although Casio doesn't release its full spec sheet, it's quite fast from my experience with it. There's quite a few built in functions that work very well with it's huge touch screen. You can even use two apps at once in split screen! The biggest con is it's build quality. It's as thick as a TI 84 Plus, but it has a resistive touch screen and abominable button quality (they're long but super thin with hardly any resistance to presses so it's super easy to click the wrong button).

Although I haven't use the Casio cg50 I think it's work looking into. It's similar to the cg500 in terms of features but a lot cheaper coming it at $112 USD it's the least expensive calculator of the ones you've listed. However it doesn't have a touch screen. It's more like an Nspire but without any CAS functionality

The Nspire CX CAS is by far the most popular by students and teachers in the US. It is quite powerful and has good community support. However it's quite difficult to get familiar enough with the interface to use it efficiently. If you end up going for this calculator I'd suggest waiting until the Nspire CX CAS II is released since it'll be over twice as fast for the same price (even if that price is quite expensive).

The HP Prime is by far the superior calculator in terms of specs, even the original HP Prime is faster than the upcoming Nspire CX CAS II. The second generation of the HP Prime (HP Prime G2) isn't sold in America yet, but even after ordering it overseas and paying shipping, the total cost is less than a full price Nspire. The HP Prime also has a touch screen, unlike the Casio cg500, it has a nice capacitive one (like the ones on smartphones). The only downside is the poor software support, the developers over at HP aren't very... motivated to add software features such as a 3D parametric grapher app.

tl;dr I think you'll be happy with any calculator you choose. It depends on what you value most. If you're concerned about price, I'd suggest the Casio cg50 or cg500. If you want a teacher-familiar calculator, the Nspire CX II is your best bet. If you're just looking for raw power, the HP Prime G2 is the way to go.

If you have any questions I'm happy to answer them!
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