curried.scala

scala> trait MyTrait extends (String => Int => Int)
defined trait MyTrait

scala> class X extends MyTrait {
     |   def apply(x: String)(i: Int): Int = 10
     | }
<console>:8: error: class X needs to be abstract, since method apply in trait Function1 of type (v1: String)Int => Int is not defined
(Note that T1 does not match String)
       class X extends MyTrait {

works.scala

scala> class X extends MyTrait {
     |  def apply(x: String): Int => Int = (x: Int) => 10
     | }
defined class X

This works:
scala> class X extends MyTrait {
| def apply(x: String): Int => Int = (x: Int) => 10
| }
defined class X