Input: Mexico City
Due in large part to the persuasion of representative Servando Teresa de Mier, Mexico City was chosen because it was the center of the country's population and history, even though Querétaro was closer to the center geographically. The choice was official on November 18, 1824, and Congress delineated a surface area of two leagues square (8,800 acres) centered on the Zocalo. This area was then separated from the State of Mexico, forcing that state's government to move from the Palace of the Inquisition (now Museum of Mexican Medicine) in the city to Texcoco. This area did not include the population centers of the towns of Coyoacán, Xochimilco, Mexicaltzingo and Tlalpan, all of which remained as part of the State of Mexico.

How large was the area the federal government would proclaim to be the capital?
Output: two leagues square (8,800 acres)

Input: Valencia
Balansiyya had a rebirth of sorts with the beginning of the Taifa of Valencia kingdom in the 11th century. The town grew, and during the reign of Abd al-Aziz a new city wall was built, remains of which are preserved throughout the Old City (Ciutat Vella) today. The Castilian nobleman Rodrigo Diaz de Vivar, known as El Cid, who was intent on possessing his own principality on the Mediterranean, entered the province in command of a combined Christian and Moorish army and besieged the city beginning in 1092. By the time the siege ended in May 1094, he had carved out his own fiefdom—which he ruled from 15 June 1094 to July 1099. This victory was immortalised in the Lay of the Cid. During his rule, he converted nine mosques into churches and installed the French monk Jérôme as bishop of the See of Valencia. El Cid was killed in July 1099 while defending the city from an Almoravid siege, whereupon his wife Ximena Díaz ruled in his place for two years.

What was El Cid's real name?
Output: Rodrigo Diaz de Vivar

Input: Lancashire
To the east of the county are upland areas leading to the Pennines. North of the Ribble is Beacon Fell Country Park and the Forest of Bowland, another AONB. Much of the lowland in this area is devoted to dairy farming and cheesemaking, whereas the higher ground is more suitable for sheep, and the highest ground is uncultivated moorland. The valleys of the River Ribble and its tributary the Calder form a large gap to the west of the Pennines, overlooked by Pendle Hill. Most of the larger Lancashire towns are in these valleys South of the Ribble are the West Pennine Moors and the Forest of Rossendale where former cotton mill towns are in deep valleys. The Lancashire Coalfield, largely in modern-day Greater Manchester, extended into Merseyside and to Ormskirk, Chorley, Burnley and Colne in Lancashire.

Where is the Lancashire Coalfield located?
Output: modern-day Greater Manchester

Input: Group (mathematics)
Mathematicians often strive for a complete classification (or list) of a mathematical notion. In the context of finite groups, this aim leads to difficult mathematics. According to Lagrange's theorem, finite groups of order p, a prime number, are necessarily cyclic (abelian) groups Zp. Groups of order p2 can also be shown to be abelian, a statement which does not generalize to order p3, as the non-abelian group D4 of order 8 = 23 above shows. Computer algebra systems can be used to list small groups, but there is no classification of all finite groups.q[›] An intermediate step is the classification of finite simple groups.r[›] A nontrivial group is called simple if its only normal subgroups are the trivial group and the group itself.s[›] The Jordan–Hölder theorem exhibits finite simple groups as the building blocks for all finite groups. Listing all finite simple groups was a major achievement in contemporary group theory. 1998 Fields Medal winner Richard Borcherds succeeded in proving the monstrous moonshine conjectures, a surprising and deep relation between the largest finite simple sporadic group—the "monster group"—and certain modular functions, a piece of classical complex analysis, and string theory, a theory supposed to unify the description of many physical phenomena.

What can be used to classify small groups even though there is no classification of all finite groups?
Output:
Computer algebra systems