Closed my old suggestion due to finding proof of higher prices. However, the lower bound needs adjustment. http://backpack.tf/vote/id/515c5b2b4bd7b8474b000015

Proof from previous suggestion: (also +42, -6 votes)

Link 1: http://www.tf2outpost.com/trade/8364668

Highest pure offer 3 buds plus bill's ~3.3, rejected

Link 2: http://www.tf2outpost.com/trade/9578014

Highest pure offer same as L1, rejected but willing to do 3.5

Link 3: http://www.tf2outpost.com/trade/9614386

Highest pure offer same as L1, "probably going to take it"

Link 4: http://www.tf2outpost.com/trade/9755540

Sold for Circling Heart Whoopee Cap + ~3 key sweets ( http://www.tf2outpost.com/trade/8899062 ) ~2.5

Buyer possibly unaware of the brainiac's price.

Link 5: http://www.tf2outpost.com/trade/9714219

Highest pure offer 3 buds pure.

Link 6: http://www.tf2outpost.com/trade/9610381 (A little odd, I know)

Planets Brainiac traded for GE Engicap, S. Gunslinger, sweets + 5 keys (?) ~3.33 buds

Newly found proof for the high bound, courtesy of Liddojunio

L1: http://www.tf2outpost.com/trade/8759221 -Sold For ~ 4 Buds

L2: http://www.tf2outpost.com/trade/9617502 Level 100 (apperently) sold for 4 buds to Roy.

I hope this suggestion is better than the last one.