Ubuntu – Quick unit-aware calculator

I want to be able to press a keyboard combination, start typing a mathematical expression that includes units and slightly advanced math (not just a four-function calculator), and get a result immediately, in units that I specify, that I can copy and paste.

• Currently I open Firefox and press Ctrl+K, type in the search box, and it usually gives me a result in the drop-down from Google Calculator. It doesn't always, though, so I press "=" at the end, wait for a result, remove the equals, wait for a result, realize it doesn't understand the way I typed a unit, open the result in a new tab, etc. it sucks.
• Wolfram Alpha is smarter, but very much slower, and the output is all images, not text, and I don't have a quick widget for it, if such a thing could even exist.
• GNU units has a ton of units, which is great, and I can define my own units, which is great, but they have to be written in specific, unintuitive ways, it doesn't handle much advanced math, and I'd need to open a terminal, start units, etc. I hate the command line.
• I wasted a lot of time trying to make front-ends for units in Deskbar and Launchy, but I'm not a real coder and I don't use either of those anymore.

Any other solutions or enhancements of these?

(Cross-platform is best)

The ideal unit-aware calculator would be able to handle all of these:

• 7 nV/sqrt(Hz) ⋅ sqrt(20000 Hz - 20 Hz) → μV = 0.99 μV
• sqrt(4*k*25 °C * 1 kΩ * (20 kHz - 20 Hz)) = 0.57357 μV
• 3.5 billion kilowatt-hours per year = 399.5 MW
• 60 billion kWh per year = 6.849 GW
• 1/sqrt(2 mH * 2 nF) = 500 kHz
• 1/(2*pi*10 kΩ * 22 µF) = 0.7234 Hz
• 1/(2·π·100 Hz·30pF) → ohm = 53.05 MΩ
• −10 dBV + 4 dB + 10 dB − 12 dB → dBu = -5.782 dBu
• 94 dBSPL → Pa = 1.00237 Pa
• 54 inches + 2 feet → cm = 198.1 cm
• 12 V ÷ 141.5 µA = 84.8 kΩ
• 16 bit * 44.1 kHz * 2 → kbit/s = 1411 kbit/s
• 1 hundred V / 5 ohms = 20 A
• furlong per fortnight → cm/minute = 0.9979
• attoparsec/microfortnight → in/second = 1.004
• 1 ft / speed of sound = 0.89576 ms