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The thing you are doing "wrong" is passing p0=None to curve_fit().

All fitting methods really, really require initial values. Unfortunately, scipy.optimize.curve_fit() has the completely unjustifiable option of allowing you to not set initial values and silently (not even a warning!!) making the absurd guess that all values have initial values of 1.0. It turns out that for your problem these impossible-to-justify-and-broken-by-design initial values are so bad that the fit fails to find a good answer. This is not uncommon. curve_fit is lying to you that p0=None is acceptable, and you are believing that lie.

The solution is to recognize that the offset is obviously around 11 and use p0=[1.0, 0.5, 0.5, 11.0].

You might consider using lmfit (https://lmfit.github.io/lmfit-py/). for this problem (disclaimer: I am a lead author). lmfit has a Model class for curve-fitting that has several useful features that might be useful here (not that curve_fit cannot solve this problem -- it can). With lmfit, your fit might look like:

You forgot that there is no implicit multiplication. Use x*y not xy

From the TI-Nspire Lua Scripting API Reference Manual 12.1 math.eval:

Warning

math.eval is not available during script initialization

To avoid this error do not call the function befor script is initialized.

Makefile is wrong

Function proc_create_data has prototype

What Egor is trying to say is that computers do not calculate exact answers most of the time.

Texas Instruments deals primarily in the micro-controllers so I wouldn't expect the usual x86-64 processor inside that device of yours. That means TI can do a whole lot of things in their own way. They may make own decisions on how to handle small values, rounding, how to handle complex mathematical operations etc...

Computers use at least 32 bit floating point numbers these days. This page gives precision (number of bits before e^-16 that are correct in the machine representation). For 32 bits that value is 24. I couldn't find much info on the calculator, except the wiki page, which says its precision is 14. More than half-float less than float, not defined in that IEEE standard.

That sqrt over there is a nasty function. Computing its value requires quite a lot of computations. Lots of steps means lots of arithmetic errors, the lower precision the further from true value it gets. This also depends on the exact algorithm chosen in the sqrt function. You could check whether the math.sqrt(4^2) returns what it should return and whether math.sqrt(4^2))/(2*4) return exactly half of that.

Battling with numerical errors in computations is an entire discipline on its own and recipes differ depending on what equation you are tackling. There's this post considering the quadratic equations.

Or maybe in your case you'll be happier with just discarding all but few numbers after the decimal point in the final answer.

From https://www.lua.org/manual/5.1/manual.html#pdf-tostring

tostring (e)

Receives an argument of any type and converts it to a string in a reasonable format. For complete control of how numbers are converted, use string.format. If the metatable of e has a "__tostring" field, then tostring calls the corresponding value with e as argument, and uses the result of the call as its result.

Maybe you should learn the very basics of Lua befor you continue using a TI NSpire's Lua API.

Also tostring is mentioned in Chapter 1, page 1 of the NSpire Lua Scripting API Reference Guide...

So maybe you should get into reading manuals. It's a good habit.

Something like this:

I suppose that you are typing something in scratchpad's calculator and teacher ask you to clear the history? Firstly, you can save the scratchpad's sessions. Press ctrl+home/file/save and TI will open a new document with your calculator and graph content, which you can save. Then, close the document, go back to scratchpad and clear the history in front of your teacher. EDIT: after careful reading, it seems i misunderstood the question. What kind of "clear" your teacher wants you to perform, hard reset? Thats a pretty complicated procedure, i really doubt that teacher is that much into TI calcs that she would know it. Please, clarify it.