Simple trick to use HTTP POST with curl to do an XQuery - (I struggled for a bit with the Content-type)
curl --header "Content-type: text/xml" --data "@x.xml" http://hostname:8080/exist/rest/db/
where x.xml is something like:
<?xml version="1.0" encoding="UTF-8"?>
<query xmlns="http://exist.sourceforge.net/NS/exist" start="1" max="20">
<text>
<![CDATA[
some XQuery here...
]]>
</text>
<properties>
<property name="indent" value="yes"/>
</properties>
</query>