My input text has the following pattens:
I want to replace it with this:
I'm trying the following expression, but it does not work:
Any ideas? Thanks.

use $1 and $6 instead of \1 and \6, see if that helps. Use single-quotes around the code unless you are on windows.

Thanks, but that does not work. By the way, I'm not using \6, but rather \n6.

Use $1 instead of \1

Modify the command as below ...
perl -p -e "s/func_a\((.*)?\);/func_b\($1,\n6\);/s" < file |more

Yes, I used $1 instead of \1. I think it makes no difference.
When I have patterns that don't have new lines in them, such as:
Doing
works as expected.

The problem is that with perl -p, you are only reading and examining a line at a time. Thus the pattern match is not being applied to anything which straddles a line boundary, even if you have the /s modifier. You can fix that by reading all lines at once, with perl -0777 or something equivalent.

See also the Perl FAQ, which has a detailed discussion of this topic.

perl should have given me an error/warning because the s modifier isn't applicable to -p.
Anyway, here's what I tried, but this time I get nothing outputted:
and