How to execute the output of a command within the current shell?

The eval command exists for this very purpose.

eval "$( ls | sed... )"

More from the bash manual:

eval

          eval [arguments]

The arguments are concatenated together
into a single command, which
is then read and executed, and its
exit status returned as the exit
status of eval. If there are no
arguments or only empty arguments, the
return status is zero.