Is there a calculator with LaTeX-syntax?

The calc package allows you to do some calculations in source, but only within commands like \setcounter and \addtolength. As far as I can tell, this is not what you want.

If you already use sage, then the sagetex package is pretty awesome (if not, it's overkill). It allows you get nicely formatted output from input like this:

The square of
$\begin{pmatrix}
1 & 2 \\
3 & 4
\end{pmatrix}$
is \sage{matrix([[1, 2], [3,4]])^2}.

The prime factorization of the current page number is \sage{factor(\thepage)}

There is a way to do what you want just not quite how you describe.

You can use the fp package (\usepackage[options]{fp}) the floating point package will do anything you want; solving equations, adding dividing and many more. Unfortunately it will not read the LaTeX math you instead have to do something a little different, the documentation is very poor so I'll give an example here.

for instance if you want to do (2x3)/5 you would type:

\FPmul\p{2}{3}           % \p is the assignment of the operation 2x3
\FPupn\p{\p{} 7 round}   % upn evaluates the assignment \p and rounds to 7dp
\FPdiv\q{\p}{5}          % divides the assigned value p by 5 names result q
\FPupn\q{\q{} 4 round}   % rounds the result to 4 decimal places and evaluates
$\frac{2\times3}{5}=\FPprint\q$  % This will print the result of the calculations in the math.

the FP commands are always ibvisible, only FPprint prints the result associated with it so your documents will not be messy, FP commands can be placed wherever you wish (not verb) as long as they are before the associated FPprint.

Considering that LaTeX itself is a Turing-complete markup language I strongly doubt you can build something like this that isn't built directly into LaTeX. Furthermore, LaTeX math matkup itself has next to no semantic meaning, it merely describes the visual appearance.

That being said, you can probably hack together something which recognizes a non-programmable subset of LaTeX math markup and spits out the result in the same way. If all you're interested in is simple arithmetics with fractions and integers (careful with decimal fractions, though, as they may appear as 3{,}141... in German texts :)) this shouldn't be too hard. But once you start with integrals, matrices, etc. I fear that LaTeX lacks expressiveness to accurately describe your intentions. It is a document preparation system, after all and thus not very suitable as input for computer algebra systems.

Side note: You can switch to Word which has—in its current version—a math markup language which is sufficiently LaTeX-like (by now it even supports LaTeX markup) and yet still Google-friendly for simpler terms:

With the free Microsoft Math add-in you can even let Word calculate expressions in-place:

There is none, because it is generally not possible.

LaTeX math mode markup is presentational markup and there are cases in which it does not provide enough information to calculate the expression.

That was one of the reasons MathML content markup was created and also why MathML is used in Mathematica. MathML actually is sort of two languages in one:

• presentation markup
• content markup

To accomplish what you are after you'll have to have MathML with comibned presentation and content markup (see MathML spec).

In my opinion your best bet is to use MathML (even if it is verbose) and convert to LaTeX when necessary. That said, I also like LaTeX syntax best and maybe what we need is a compact syntax for MathML (something similar in spirit to RelaxNG compact syntax).

IIRC Mathematica can do it.

The latex2sympy2 Python library can parse LaTeX math expressions.

from latex2sympy2 import latex2sympy

tex_str = r"""YOUR TEX MATH HERE"""
tex_str = r"\frac{9\pi}{\ln(12)}+22"  # example TeX math

sympy_object = latex2sympy(tex_str)
evaluated_tex = float(sympy_object.evalf())
print(evaluated_tex)

This Python 3 code evaluates 9/ln(12)+22 (in its LaTeX from above) to 33.37842899841745.

The snippet above only handles basic algebraic simplification (math expressions without variables). Since the library converts LaTeX math to SymPy objects, the above code can easily be tweaked and extended to handle much more complicated LaTeX math (including solving derivatives, integrals, etc...).

The latex2sympy2 library can be installed via the pip command: pip install --user latex2sympy2