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BIG-Bench Extra Hard (BBEH) / Consider the following new operations:

Problem

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input

Consider the following new operations: a<>ba <> b equals $(a * a) + b$ if b<2b < 2 and $(b * b) + a$ otherwise. a!ba ! b equals (a+b)(a + b) if a−b>0a - b > 0; otherwise, it equals −a+−b-a + -b. $a @ b$ equals (a+b)(a + b) if a<>b>0a <> b > 0; otherwise, it equals a−ba - b. a><ba >< b equals (a−b)(a - b) if a+b>0a + b > 0; otherwise, it equals a+ba + b. For brevity, we use a<op1><op2>ba <op1><op2> b to denote (aop1b)op2b(a op1 b) op2 b. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$. Let A = (((((((((((((((((-10 *+ nine) <> four) @ 6) ! -10) -!+ -2) @ -2) ><<>+ -6) -@>< -9) ><* 1) <>@ five) +! -1) ! 8) -* 6) -><+ -3) ><@>< 3) +-+ nine) >< four) Let B = ((((-3 @ -8) -<> (two <> -6)) *-- ((-5 >< -1) -- (4 - 3))) ++ (((ten @ -3) *@+ (10 *@- 6)) ><>< ((-6 <>@<> 5) >< (7 *- -2)))) Let C = ((((-3 +*+ 2) + (8 -* -10)) *- ((-9 ->< -3) @- (10 <>- -8))) !- (((-4 <> -6) @! (-1 **>< nine)) - ((two @! five) @<>! (7 !+ -1)))). Compute A + B - C. Your final answer must be in number form.
Plain-text mathematical notation (without MathML)
Consider the following new operations:

a<>b equals $(a * a) + b$ if b<2 and $(b * b) + a$ otherwise.
a!b equals (a+b) if a−b>0; otherwise,  it equals −a+−b.
$a @ b$ equals (a+b) if a<>b>0; otherwise,  it equals a−b.
a><b equals (a−b) if a+b>0; otherwise,  it equals a+b.
For brevity, we use a<op1><op2>b to denote (aop1b)op2b. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.
Let A = (((((((((((((((((-10 *+ nine) <> four) @ 6) ! -10) -!+ -2) @ -2) ><<>+ -6) -@>< -9) ><* 1) <>@ five) +! -1) ! 8) -* 6) -><+ -3) ><@>< 3) +-+ nine) >< four)
Let B = ((((-3 @ -8) -<> (two <> -6)) *-- ((-5 >< -1) -- (4 - 3))) ++ (((ten @ -3) *@+ (10 *@- 6)) ><>< ((-6 <>@<> 5) >< (7 *- -2))))
Let C = ((((-3 +*+ 2) + (8 -* -10)) *- ((-9 ->< -3) @- (10 <>- -8))) !- (((-4 <> -6) @! (-1 **>< nine)) - ((two @! five) @<>! (7 !+ -1)))).
Compute A + B - C. Your final answer must be in number form.
Original LaTeX notation
Consider the following new operations:

$a <> b$ equals $(a * a) + b$ if $b < 2$ and $(b * b) + a$ otherwise.
$a ! b$ equals $(a + b)$ if $a - b > 0$; otherwise,  it equals $-a + -b$.
$a @ b$ equals $(a + b)$ if $a <> b > 0$; otherwise,  it equals $a - b$.
$a >< b$ equals $(a - b)$ if $a + b > 0$; otherwise,  it equals $a + b$.
For brevity, we use $a <op1><op2> b$ to denote $(a op1 b) op2 b$. For example, $4 +* -5$ means $(4 + -5) * -5$ and $4 *-- -5$ means $(4 * -5) -- -5$.
Let A = (((((((((((((((((-10 *+ nine) <> four) @ 6) ! -10) -!+ -2) @ -2) ><<>+ -6) -@>< -9) ><* 1) <>@ five) +! -1) ! 8) -* 6) -><+ -3) ><@>< 3) +-+ nine) >< four)
Let B = ((((-3 @ -8) -<> (two <> -6)) *-- ((-5 >< -1) -- (4 - 3))) ++ (((ten @ -3) *@+ (10 *@- 6)) ><>< ((-6 <>@<> 5) >< (7 *- -2))))
Let C = ((((-3 +*+ 2) + (8 -* -10)) *- ((-9 ->< -3) @- (10 <>- -8))) !- (((-4 <> -6) @! (-1 **>< nine)) - ((two @! five) @<>! (7 !+ -1)))).
Compute A + B - C. Your final answer must be in number form.

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Source and history

task_id
66a34439-0ab3-55bd-a3e0-431acc41c17b
task_key
bbeh~5fmultistep~5farithmetic--full--66a34439-0ab3-55bd-a3e0-431acc41c17b
task_revision_id
1
config / split
bbeh_multistep_arithmetic / full

Official source

initial import