wrapfigures and quote environment not working together

Question

I want to have a figure floating next to a block quote. So I used the wrapfig package and the quote environment.

If you typeset the following example, you will see that the figure is printed on the next page instead of being next to the block quote. It works perfectly with normal text. Is there any solution to that?

\documentclass{article}
\usepackage[english]{babel}
\usepackage{blindtext}
\usepackage{wrapfig}
\begin{document}
    \blindtext[3]
    \begin{wrapfigure}{R}{0.5\textwidth}
        \centering
        \rule{5cm}{5cm}
        \caption{Foo bar foobar baz baq}
    \end{wrapfigure}
    \begin{quote}
        \blindtext
    \end{quote}
    \blindtext
\end{document}

Answer 1

It seems to work OK using r instead of R (lowercase specifiers don't allow the object to float); I also added some value for the hanging indentation:

\documentclass{article}
\usepackage[english]{babel}
\usepackage{blindtext}
\usepackage{wrapfig}
\begin{document}
    \blindtext[3]
    \begin{wrapfigure}{r}[-10pt]{0.5\textwidth}
        \vspace*{\topsep}
        \centering
        \rule{5cm}{5cm}
        \caption{Foo bar foobar baz baq}
    \end{wrapfigure}
    \begin{quote}
        \blindtext
    \end{quote}
    \blindtext
\end{document}

Notice the additional \vspace*{\topsep} inside wrapfigure; in this case, this is necessary to have the top of the figure aligned with the top of the first line of the quote environment (thanks to barbara beeton for suggesting this improvement).