###########################################################
#
#  Example showing how to use the Parser to make
#  a formula that you can evaluate and print in TeX form.
#

DOCUMENT();        # This should be the first executable line in the problem.

loadMacros(
  "PGbasicmacros.pl",
  "PGanswermacros.pl",
  "Parser.pl",
);

TEXT(beginproblem());

###########################################################
#
#   Use  standard numeric mode
#
Context('Numeric');

#
#   Define some functions
#
$a = non_zero_random(-8,8,1);
$b = random(1,8,1);

@f = (
    "1 + $a*x + $b x^2", 
    "$a / (1 + $b x)",
    "$a x^3 + $b",
    "($a - x) / ($b + x^2)"
);

#
#  Pick one at random
#
$k = random(0,$#f,1);
$f = Formula($f[$k])->reduce;

#
#  Where to evaluate it
#
$x = random(-5,5,1);

###########################################################
#
#  The problem text
#
BEGIN_TEXT

If \(\displaystyle f(x) = \{$f->TeX\}\) then \(f($x)=\) \{ans_rule(10)\}.

END_TEXT

###########################################################
#
#  The answer
#
ANS(num_cmp($f->eval(x=>$x)));
$showPartialCorrectAnswers = 1;

###########################################################

ENDDOCUMENT();        # This should be the last executable line in the problem.