Any discussion of Wolfram Alpha should start with Wolfram's flagship and source of dominance in the universe: Mathematica®, upon which I imagine Alpha is built.  There are any number of categories of software that leave me amazed that such works of accomplishment can even spawn from the limited human mind: regular expression parsers, C++ compilers, natural language processing.  Voice recognition used to fall into that realm until I figured out how it works. But Mathematica sits at the apex, the crowning achievement of software engineering. It's nothing at all like Matlab, which is plain old functional programming. It's something else.  Several times during my software engineering career, I contemplated working there just to see the source code.

Wolfram Alpha, then, is something like a search engine, except instead of simply looking up words, it answers questions.

With the introductions out of the way, let's go back a few decades to when I originally wrote A Hierarchy of Gods. I might have had Mathematica at the time, a story in itself, but there was nothing like Alpha. There may not even have been a search engine like Google or Duck Duck Go, and I had to pick a date in the latter 21st century where the line from Earth to Mars ran approximately opposite to the direction to Orion's shield. I had to know how far apart Earth and Mars were at that time. I had to know how long it would take, considering special relativity, to go 32 light-years at a constant 0.8g acceleration, in both ship time and "real" time, with and without turn-around. I had my math cut out for me.

For the first part, I had to find out where Earth and Mars were currently and apply a lot of orbital mechanics and trigonometry to figure out all the angles until I found a date that placed them where I wanted, then apply some more math to calculate the distance distance between them, then some more to figure out travel time. Hours or days. The math, not the travel time. But that was then, and this is now. You need a right ascension to Mars of about 17 hours, so go to Wolfram Alpha here and start plugging in some dates:

location Mars May 15, 2074

And you get this (near right). Wow! Not only what I asked for, but I find out that the date is on a Tuesday, get a schematic of the entire solar system, a view as Mars appears in the sky, and rising at setting times in Luxemburg (that's where it thinks I am). Mars is in Leo on May 15, 2074. No good, so I try again.  I don't remember exactly what date I picked for the novel and don't want to hunt for old notes, so let's pretend it was May 15, 2095.

distance Earth Mars May 15, 2095

Again, I get more than I asked for (far right). I see that the distance is 79.57 million kilometers, coincidentally a near minimum, and as a bonus, I find out that the time for a radio signal to cross that distance is 4.424 minutes. I might need to know that. From here, it's trivial to calculate constant-acceleration flight times, but to get to this point, I have consumed less like hours or days and more like two minutes. Oh, had there been Wolfram Alpha in the old days!

Unfortunately, Alpha could not have helped me with the calculus for my relativistic calculations. Alas! Not that it can't do calculus, but it isn't able to formulate a system that complicated it its digital head from the description you give it. It's not as as smart yet as the Enterprise's computer on Star Trek, but it's getting there. Not to worry. When I first started this site, I wrote the relativistic equations down as an early post, not only for your edification, but so that I wouldn't have to figure them out all over again.

And it's not just astronomy.

In: Copernicium isotopes
Out: Unstable:
Cn-285 (40 min) | Cn-283 (4.17 min) | Cn-284 (31 s) | 
Cn-282 (30 s) | Cn-281 (10 s) | Cn-280 (1 s) | Cn-279 (100 ms) | 
Cn-278 (10 ms) | Cn-277 (1.1 ms)

Nor is it just for science fiction.  Suppose you're writing an international spy thriller:

In: Population Cluj County Romania
Out: Cluj, Romania | 698929 people (3.3% of total for Romania) (2014 estimate) Romania | 
19.7 million people (world rank: 59th) (2017 estimate)

Or a murder mystery requiring forensics:

In: percentage phosphorus human body
Out: 1.1 mass%

Or a WWII submarine adventure:

In: 550 feet ocean depth
Out: depth | 550 feet temperature | 16.4 °C (degrees Celsius) salinity |
35 psu (practical salinity units)
overpressure | 16.89 bars = 16.67 atm (atmospheres) = 1689 kPa (kilopascals) density |
1.026 g/cm^3 (grams per cubic centimeter) = 64.08 lb/ft^3 (pounds per cubic foot) = 
1026 kg/m^3 (kilograms per cubic meter)
sound speed | 1514 m/s (meters per second) = 4967 ft/s (feet per second) = 
5450 km/h (kilometers per hour)
(assuming pressure-depth relation for standard ocean)

Whoa! Sound speed! That's information we might need for sonar.

Of course, Alpha can't do everything. Sometimes you get that dreaded response that it doesn't know how to interpret your input (which I couldn't make it do for the purpose of this post despite trying for several minutes), in which case you can rephrase your question and try again. There is a pro version that keeps tempting me that might be a little smarter; I  haven't tried it.  Applications like Cartes du Ciel give you better sky charts, and Google Maps will give you the railroad travel time from Nizhny Novgorod to Vladivostok (about six days), but for the subjects it knows, Wolfram Alpha can seem like magic. Give it a try, and let us know what you think.