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

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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 $(b * a) + b$ if |a−b|<2|a-b| < 2 and $(a * b) + a$ otherwise. a<>ba <> b equals (a−b)(a - b) if $a * b > 0$; 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. $a & b$ 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 = ((((-5 !@<> 3) & (1 & -9)) <><> ((8 +* -5) -+ (six ><++ 2))) <> (((-7 !- four) @-! (-6 ! -5)) -@ ((1 ! 1) *- (nine <>*& 10)))) Let B = (((((((((((((((((((-5 -+- nine) &*! -2) & -4) <> three) -+<> -5) @@! nine) &* 8) *<> -4) &+! two) & 7) & 4) + -3) &&! -1) ! -9) + 9) - -6) @ -5) *! -4) !-- -9) Let C = ((((-4 &*& 3) *<> (-6 @** 7)) -& ((four *+ -6) <>@<> (-6 ! -8))) --@ (((-8 - -1) ><@ (-2 &<>@ 3)) <> ((-10 <>! ten) -<>- (2 <>@- -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 $(b * a) + b$ if |a−b|<2 and $(a * b) + a$ 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 = ((((-5 !@<> 3) & (1 & -9)) <><> ((8 +* -5) -+ (six ><++ 2))) <> (((-7 !- four) @-! (-6 ! -5)) -@ ((1 ! 1) *- (nine <>*& 10))))
Let B = (((((((((((((((((((-5 -+- nine) &*! -2) & -4) <> three) -+<> -5) @@! nine) &* 8) *<> -4) &+! two) & 7) & 4) + -3) &&! -1) ! -9) + 9) - -6) @ -5) *! -4) !-- -9)
Let C = ((((-4 &*& 3) *<> (-6 @** 7)) -& ((four *+ -6) <>@<> (-6 ! -8))) --@ (((-8 - -1) ><@ (-2 &<>@ 3)) <> ((-10 <>! ten) -<>- (2 <>@- -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 $(b * a) + b$ if $|a-b| < 2$ and $(a * b) + a$ 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 = ((((-5 !@<> 3) & (1 & -9)) <><> ((8 +* -5) -+ (six ><++ 2))) <> (((-7 !- four) @-! (-6 ! -5)) -@ ((1 ! 1) *- (nine <>*& 10))))
Let B = (((((((((((((((((((-5 -+- nine) &*! -2) & -4) <> three) -+<> -5) @@! nine) &* 8) *<> -4) &+! two) & 7) & 4) + -3) &&! -1) ! -9) + 9) - -6) @ -5) *! -4) !-- -9)
Let C = ((((-4 &*& 3) *<> (-6 @** 7)) -& ((four *+ -6) <>@<> (-6 ! -8))) --@ (((-8 - -1) ><@ (-2 &<>@ 3)) <> ((-10 <>! ten) -<>- (2 <>@- -1)))).
Compute A + B - C. Your final answer must be in number form.

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Source and history

task_id
afea2b6a-18dd-541e-8fd0-94777ef2f127
task_key
bbeh~5fmultistep~5farithmetic--full--afea2b6a-18dd-541e-8fd0-94777ef2f127
task_revision_id
1
config / split
bbeh_multistep_arithmetic / full

Official source

initial import