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\documentclass{article}
\usepackage{tcolorbox}
\usepackage{xsim}
\usepackage{needspace}
\DeclareExerciseEnvironmentTemplate{custom}
{%
\Needspace*{5\baselineskip}
\begin{tcolorbox}
\textbf{\XSIMmixedcase{\GetExerciseName}~\GetExerciseProperty{counter}.}%
\GetExercisePropertyT{subtitle}{ \textit{#1}}%
\end{tcolorbox}
\noindent
}
{\vspace{\baselineskip}}
\xsimsetup{exercise/template = custom}
\usepackage{lipsum}
\begin{document}
\begin{exercise}[subtitle=Foo bar baz]
\lipsum[1]
\end{exercise}
\lipsum[2]
\end{document}
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