% https://tex.stackexchange.com/q/369065/
\documentclass{article}
\usepackage{xsim,tcolorbox,needspace}

\xsimsetup{
  exercise/within=section ,
  exercise/the-counter = \thesection.\arabic{exercise} ,
  exercise/template=cyan-box ,
  exercise/name=Example ,
  solution/template=red ,
  solution/print=true
}

\DeclareExerciseEnvironmentTemplate{cyan-box}
  {%
    \begin{tcolorbox}[arc=0mm,boxrule=1pt,colback=white,colframe=cyan,leftrule=3mm]
      \textsf{%
        \MakeUppercase{%
          \XSIMmixedcase{\GetExerciseName}~\GetExerciseProperty{counter}%
        }%
      }%
      \GetExercisePropertyT{subtitle}{ \textit{#1}}%
      \quad
  }
  {\end{tcolorbox}}

\DeclareExerciseEnvironmentTemplate{red}
  {%
    \par
    \Needspace*{2\baselineskip}
    \noindent
    \textsf{\textcolor{red}{\MakeUppercase{\XSIMmixedcase{\GetExerciseName}}}}%
    \quad
  }
  {\par\bigskip}

\begin{document}

\section{My first set of exercises}
\begin{exercise}
  Prove that $\frac{1}{2}\Delta(f_{ij}f^{ij})
  =\nabla^{k}f^{ij}+f^{ij}f^{k}[2\nabla_{i}R_{jk}-\nabla_{k}R_{ij}]$
\end{exercise}
\begin{solution}
  From \dots
\end{solution}

\begin{exercise}
  Prove that Paulinho is smart.
\end{exercise}
\begin{solution}
  All ducks are smart. Paulinho is a duck. Therefore, Paulinho is smart.
\end{solution}

\begin{exercise}
  Prove that Paulinho is smart.
\end{exercise}
\begin{solution}
  All ducks are smart. Paulinho is a duck. Therefore, Paulinho is smart.
\end{solution}

\section{My second set of exercises}
\begin{exercise}
  Prove that Paulinho is smart.
\end{exercise}
\begin{solution}
  All ducks are smart. Paulinho is a duck. Therefore, Paulinho is smart.
\end{solution}

\begin{exercise}
  Prove that Paulinho is smart.
\end{exercise}
\begin{solution}
  All ducks are smart. Paulinho is a duck. Therefore, Paulinho is smart.
\end{solution}

\end{document}
