A small inconvenience is that in order to use sagetex you have to:

1. run pdflatex sagetex_example
2. run sage sagetex_example.sagetex.sage
3. run pdflatex sagetex_example again

Running sage in between is only a small inconvenience. The problems with the sage verbatim environments are more serious:

• Inline environments can not be used to assign to variables
• Multiline environments are equivalent to verbatim environments, which mess up with AMC seriously
• It is crucial to define variables to do really meaningful examples

Partial+inconvenient workaround: combine latex variables and sage commands. Example:

\element{T1q1}{
\FPeval\a{trunc(6 + random * 3,0)}
\FPeval\b{10-\a}

\begin{question}{T1q1}

  Statement of the question:

\a, $\a$, \sage{2+3}, \sage{\a}, \sage{\b}, \sage{2+\a}

  \AMCOpen{lines=2, dots=False}{
\wrongchoice[0]{0}\scoring{0}
\wrongchoice[0.5]{0.5}\scoring{0.5}
\wrongchoice[1]{1}\scoring{1}
\wrongchoice[1.5]{1.5}\scoring{1.5}
\wrongchoice[2]{2}\scoring{2}
}
\explain{
Solution is

\sageplot[width=10cm]{plot(sin(x), 0, pi)}

\sageplot[width=10cm]{plot(\a*sin(x), 0, pi)}
}
\end{question}
}

I guess I should be happy, since this is better than fpeval alone, but it is not possible to store a polynomial, matrix, function, etc in an fpeval variable.

Much better, I added a sageraw environment to sagetex.sty

\newcommand{\sagerawline}[1]{\ST@wsf{\%
try:^^J
 _st_.current_tex_line = \the\inputlineno^^J
 #1^^J\%
except:^^J
 _st_.goboom(\the\inputlineno)}\%
\stepcounter{ST@inline}}

(note: the \% go without a backslash, but this forum complains if I leave the percentage sign alone)

and now I can define variables within latex

\sagerawline{m=randint(10,20)}

Then make computations and plots

\sage{Combinations(100,m).cardinality()}

My limited knowledge of latex does not allow me to do multiline sage raw input without relying on verbatim. I understand the problem is not easy even for the latex masters.

My sagerawline also breaks sageplot in DOC-corrige (although it works in DOC-sujet), but this can be done in other ways.

Not perfect, but this will suffice: each student gets a different question, but we are not limited to basic arithmetic.

This could be done with any other script language (at least haskell and R had latex extensions before Sage did).