#Ruby (176 chars):

Following Tony H.'s example of using hard-coded page numbers, here's what I got:

require'open-uri';b=0;(1..29).each{|i|d=open("http://stackoverflow.com/questions?sort=featured&page=#{i}").read;b+=d.scan(/<.*>\+(\d+)<.*>/).map{|x|x[0].to_i}.reduce 0,:+};p b

gave me 35300 at the time of writing.

Ruby (176 chars):

Following Tony H.'s example of using hard-coded page numbers, here's what I got:

require'open-uri';b=0;(1..29).each{|i|d=open("http://stackoverflow.com/questions?sort=featured&page=#{i}").read;b+=d.scan(/<.*>\+(\d+)<.*>/).map{|x|x[0].to_i}.reduce 0,:+};p b

gave me 35300 at the time of writing.