This blog post explains the package structure and imports a la carte in scalaz7 in detail: http://eed3si9n.com/learning-scalaz-day13
For your specific examples, for 3.failure[String] you'd need:
import scalaz.syntax.validation._
Validation already has a method ap
:
scala> "hello".successNel[Int] ap ((s: String) => "x"+s).successNel[Int]
res1: scalaz.Validation[scalaz.NonEmptyList[Int],java.lang.String] = Success(xhello)
To get the <*> operator, you need this import:
import scalaz.syntax.applicative._
Then you can do:
"hello".successNel[Int] <*> ((s: String) => "x"+s).successNel[Int]