One of the best examples of why it is so great to use Scala for API design is BigInt. Using BigInt in Java is a real headache because of the limitations of Java with regards to API design. Scala in comparison makes using BigInt no different than using Ints (with execution that there is not a BigInt literal).
// BigInt objects can be created from ints
scala> val x = BigInt(1500)
x: BigInt = 1500
// or longs
scala> val y = BigInt(**********L)
y: BigInt = **********
// or strings
scala> val z = BigInt("1234566789008723457802308972345723470589237507")
z: BigInt = 1234566789008723457802308972345723470589237507
// then thanks to scala you can multiply/divide/add/subtract etc...
// as if it was a Scala literal
scala> x * y * z
res0: BigInt = 16368874569886254973831932331037537269641764816982396175500
// by importing implicits you can also directly multiply big ints with integers and longs
// however remember to put the big in first so that the int is converted to big int
// because you cannot do Int * BigInt. It must be BigInt * Int
scala> import BigInt._
import BigInt._
scala> x * y * z * 124
res1: BigInt = 2029740446665895616755159609048654621435578837305817125762000
