Though I’m not positive the answer shouldn’t have been 91 instead

^$n means 0 .. $n - 1; so try:

say [+] ^$n+1;
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Not sure about precedence, so it might need brackets. Or maybe:

say [+] ^++$n;
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More fun! Thanks. Parens work. Probably another way that I don’t know too.

> say [+] ^1+$n
14
> say [+] ^++$n+1
15
> say [+] ^($n+1)
91
> say [+] ^++$n
105
> say [+] ^$n++
105
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»»» This post is about alpha status Perl 6, not rock solid Perl 5 «««

say [+] 1 .. prompt('Number?');
#  While you read this, try to dance (<-- fulfilling assignment requir
+ements)
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»ö« ^{. o O ( "the celebrity tell-all of the Perl-6 cult?" )}

say [+] ^$n,$n

(You do not want to change $n, so ++ is out of the question)

Also note that currently $n cannot be a native int when using ++, though that will be fixed.

$ perl6 -e'my Int $n = 10; say ++$n;'
11
$ perl6 -e'my int $n = 10; say ++$n;'
Cannot assign to an immutable value
  in sub prefix:<++> at src/gen/m-CORE.setting:5565
  in block <unit> at -e:1
$ perl6 -e'my int $n = 10; say [+] ^$n'
45
$ perl6 -e'my int $n = 10; say [+] ^$n,$n'
55
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Enjoy, Have FUN! H.Merijn

I read "to" in the OP as TO, not UPTO AND INCLUDING.

The OP also did not specify what language to give the solution in, hence the short perl6.