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When you write:

sage: f(x)=0^x

You define a "symbolic function":

sage: type(f)
<type 'sage.symbolic.expression.Expression'>
sage: f.parent()
Callable function ring with argument x

This is a kind of mathematical formula (like exp(cos(pi)) + log(x)). This is an object you can derivate, integrate, and so on.

Instead you can define a Python function:

sage: def f(x):
....:     return 0^x
sage: f(0)
1
sage: type(f)
<type 'function'>

For such easy-to-define function, you can be shorter, by typing:

sage: f = lambda x : 0^x
sage: f(0)
1
sage: type(f)
<type 'function'>

When you write:

sage: f(x)=0^x

You define a "symbolic function":

sage: type(f)
<type 'sage.symbolic.expression.Expression'>
sage: f.parent()
Callable function ring with argument x

This is a kind of mathematical formula (like exp(cos(pi)) + log(x)). This is an object you can derivate, integrate, and so on.

Instead you can define a Python function:

sage: def f(x):
....:     return 0^x
sage: f(0)
1
sage: type(f)
<type 'function'>

For such easy-to-define function, you can be shorter, by typing:

sage: f = lambda x : 0^x
sage: f(0)
1
sage: type(f)
<type 'function'>

When you write:

sage: f(x)=0^x

You define a "symbolic function":

sage: type(f)
<type 'sage.symbolic.expression.Expression'>
sage: f.parent()
Callable function ring with argument x

This is a kind of mathematical formula (like exp(cos(pi)) + log(x)). This is an object you can derivate, integrate, and so on.

Instead you can define a Python function:

sage: def f(x):
....:     return 0^x
sage: f(0)
1
sage: type(f)
<type 'function'>

For such easy-to-define function, you can be shorter, by typing:

sage: f = lambda x : 0^x
sage: f(0)
1
sage: type(f)
<type 'function'>

EDIT

According to your comment, it seems i misunderstood your question. So, the problem is not about evaluating f but about SR(0)^SR(0) being not defined. Thanks for reporting, @kcrisman opened trac ticket 18088.

When you write:

sage: f(x)=0^x

You define a "symbolic function":

sage: type(f)
<type 'sage.symbolic.expression.Expression'>
sage: f.parent()
Callable function ring with argument x

This is a kind of mathematical formula (like exp(cos(pi)) + log(x)). This is an object you can derivate, integrate, and so on.

Instead you can define a Python function:

sage: def f(x):
....:     return 0^x
sage: f(0)
1
sage: type(f)
<type 'function'>

For such easy-to-define function, you can be shorter, by typing:

sage: f = lambda x : 0^x
sage: f(0)
1
sage: type(f)
<type 'function'>

EDIT

According to your comment, it seems i misunderstood your question. So, Actually, the problem is not about evaluating the symbolic function f but about SR(0)^SR(0) being not defined. Thanks for reporting, @kcrisman opened trac ticket 18088.